<PAGE>   1

                                  UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION

                             WASHINGTON, D.C. 20549

                                    FORM 10-Q

          [ X ] QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE
                         SECURITIES EXCHANGE ACT OF 1934

                  For the Quarterly Period Ended March 31, 2001

                                       OR

          [ ] TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE
                         SECURITIES EXCHANGE ACT OF 1934

   For the Transition Period from ___________________ to _____________________

                         Commission File Number 0-13546

                               ------------------

                     APACHE OFFSHORE INVESTMENT PARTNERSHIP
                     --------------------------------------
             (Exact Name of Registrant as Specified in Its Charter)

                  Delaware                                41-1464066
       -------------------------------              ----------------------
       (State or Other Jurisdiction of                 (I.R.S. Employer
        Incorporation or Organization)              Identification Number)

       Suite 100, One Post Oak Central                    77056-4400
                                                          ----------
      2000 Post Oak Boulevard, Houston, TX                (Zip Code)
   ----------------------------------------
   (Address of Principal Executive Offices)

       Registrant's Telephone Number, Including Area Code: (713) 296-6000

Indicate by check mark whether the registrant (1) has filed all reports required
to be filed by Section 13 or 15(d) of the Securities Exchange Act of 1934 during
the preceding 12 months (or for such shorter period that the registrant was
required to file such reports), and (2) has been subject to such filing
requirements for the past 90 days.

                         YES  [X]         NO  [ ]
                             -----           -----

<PAGE>   2

                        PART I -- FINANCIAL INFORMATION

ITEM 1 -- FINANCIAL STATEMENTS

                     APACHE OFFSHORE INVESTMENT PARTNERSHIP
                               STATEMENT OF INCOME
                                   (UNAUDITED)

<TABLE>
<CAPTION>
                                                         FOR THE THREE MONTHS
                                                           ENDED MARCH 31,
                                                      --------------------------
                                                         2001            2000
                                                      ----------      ----------
<S>                                                   <C>             <C>
REVENUES:
  Oil and gas sales                                   $3,992,734      $2,534,975
  Interest income                                         17,089          36,682
                                                      ----------      ----------
                                                       4,009,823       2,571,657
                                                      ----------      ----------

EXPENSES:
  Depreciation, depletion and amortization               741,789         659,037
  Lease operating expense                                136,395         143,606
  Administrative                                         135,000         135,000
                                                      ----------      ----------
                                                       1,013,184         937,643
                                                      ----------      ----------

NET INCOME                                            $2,996,639      $1,634,014
                                                      ==========      ==========

NET INCOME ALLOCATED TO:
  Managing Partner                                    $  698,709      $  420,180
  Investing Partners                                   2,297,930       1,213,834
                                                      ----------      ----------

                                                      $2,996,639      $1,634,014
                                                      ==========      ==========

NET INCOME PER INVESTING PARTNER UNIT                 $    2,036      $    1,072
                                                      ==========      ==========

WEIGHTED AVERAGE INVESTING PARTNER
  UNITS OUTSTANDING                                      1,128.5         1,132.5
                                                      ==========      ==========
</TABLE>



                 The accompanying notes to financial statements
                     are an integral part of this statement.


                                       1
<PAGE>   3

                     APACHE OFFSHORE INVESTMENT PARTNERSHIP
                             STATEMENT OF CASH FLOWS
                                   (UNAUDITED)

<TABLE>
<CAPTION>
                                                                       FOR THE THREE MONTHS
                                                                         ENDED MARCH 31,
                                                                   ----------------------------
                                                                      2001             2000
                                                                   -----------      -----------
<S>                                                                <C>              <C>
CASH FLOWS FROM OPERATING ACTIVITIES:
  Net income                                                       $ 2,996,639      $ 1,634,014
  Adjustments to reconcile net income to net cash
     provided by operating activities:
        Depreciation, depletion and amortization                       741,789          659,037
        Changes in operating assets and liabilities:
          Decrease in accrued revenues receivable                      140,275            3,293
          Increase (decrease) in accrued operating expenses             33,651          (55,014)
          Increase (decrease) in payable to Apache Corporation        (389,176)         243,123
                                                                   -----------      -----------
        Net cash provided by operating activities                    3,523,178        2,484,453
                                                                   -----------      -----------

CASH FLOWS FROM INVESTING ACTIVITIES:
  Additions to oil and gas properties                                 (462,132)        (724,462)
  Non-cash portion of oil and gas property additions                  (136,000)        (131,747)
                                                                   -----------      -----------
        Net cash used in investing activities                         (598,132)        (856,209)
                                                                   -----------      -----------

CASH FLOWS FROM FINANCING ACTIVITIES:
  Distributions to Investing Partners                               (2,256,977)      (2,264,978)
  Distributions to Managing Partner, net                              (313,978)        (404,243)
                                                                   -----------      -----------

        Net cash used in financing activities                       (2,570,955)      (2,669,221)
                                                                   -----------      -----------

NET INCREASE (DECREASE) IN CASH AND CASH EQUIVALENTS                   354,091       (1,040,977)

CASH AND CASH EQUIVALENTS, BEGINNING OF YEAR                         1,442,878        2,748,812
                                                                   -----------      -----------

CASH AND CASH EQUIVALENTS, END OF PERIOD                           $ 1,796,969      $ 1,707,835
                                                                   ===========      ===========
</TABLE>



                 The accompanying notes to financial statements
                     are an integral part of this statement.


                                       2
<PAGE>   4

                     APACHE OFFSHORE INVESTMENT PARTNERSHIP
                                  BALANCE SHEET
                                   (UNAUDITED)

<TABLE>
<CAPTION>
                                                                    MARCH 31,        DECEMBER 31,
                                                                      2001               2000
                                                                  -------------      -------------
<S>                                                               <C>                <C>
                                           ASSETS

CURRENT ASSETS:
  Cash and cash equivalents                                       $   1,796,969      $   1,442,878
  Accrued revenues receivable                                           884,023          1,024,298
                                                                  -------------      -------------
                                                                      2,680,992          2,467,176
                                                                  -------------      -------------

OIL AND GAS PROPERTIES, on the basis of full cost accounting:
  Proved properties                                                 173,840,528        173,378,396
  Less -- Accumulated depreciation, depletion and amortization     (167,871,882)      (167,130,093)
                                                                  -------------      -------------
                                                                      5,968,646          6,248,303
                                                                  -------------      -------------
                                                                  $   8,649,638      $   8,715,479
                                                                  =============      =============

                              LIABILITIES AND PARTNERS' CAPITAL

CURRENT LIABILITIES:
  Accrued exploration and development                             $     375,000      $     511,000
  Accrued operating expenses                                            118,435             84,784
  Payable to Apache Corporation                                           2,079            391,255
                                                                  -------------      -------------
                                                                        495,514            987,039
                                                                  -------------      -------------

PARTNERS' CAPITAL:
  Managing Partner                                                      736,812            352,081
  Investing Partners (1,128.5 units outstanding)                      7,417,312          7,376,359
                                                                  -------------      -------------
                                                                      8,154,124          7,728,440
                                                                  -------------      -------------
                                                                  $   8,649,638      $   8,715,479
                                                                  =============      =============
</TABLE>



                 The accompanying notes to financial statements
                    are an integral part of this statement.


                                       3
<PAGE>   5

                     APACHE OFFSHORE INVESTMENT PARTNERSHIP
                          NOTES TO FINANCIAL STATEMENTS
                                   (UNAUDITED)


    The financial statements included herein have been prepared by the Apache
Offshore Investment Partnership (the Partnership), without audit, pursuant to
the rules and regulations of the Securities and Exchange Commission, and reflect
all adjustments which are, in the opinion of management, necessary for a fair
statement of the results for the interim periods, on a basis consistent with the
annual audited financial statements. All such adjustments are of a normal,
recurring nature. Certain information, accounting policies, and footnote
disclosures normally included in financial statements prepared in accordance
with generally accepted accounting principles have been omitted pursuant to such
rules and regulations, although the Partnership believes that the disclosures
are adequate to make the information presented not misleading. These financial
statements should be read in conjunction with the financial statements and the
summary of significant accounting policies and notes thereto included in the
Partnership's latest annual report on Form 10-K.

1.  PAYABLE TO APACHE CORPORATION

    Payable to Apache Corporation, the Partnership's managing partner (Apache or
the Managing Partner), represents the net result of the Investing Partners'
revenue and expenditure transactions in the current month. Generally, cash in
this amount will be transferred to Apache in the month after the Partnership's
transactions are processed and the net results of operations are determined.

2.  RIGHT OF PRESENTMENT

    As provided in the Partnership Agreement, as amended (the Amended
Partnership Agreement), a first right of presentment offer for 2001 of $9,928
per Unit, plus interest to the date of payment, was made to Investing Partners
in April 2001, based on a valuation date of December 31, 2000. The Partnership
is not in a position to predict how many Units will be presented for repurchase
under the April 2001 offer and cannot, at this time, determine if the
Partnership will have sufficient funds available to repurchase all Units
presented. The Investing Partners have until May 23, 2001 to offer their Units
under the current right of presentment. The Partnership has no obligation to
purchase any Units presented to the extent it determines that it has
insufficient funds for such purchases. The Amended Partnership Agreement
contains limitations on the number of Units that the Partnership can repurchase,
including a limit of 10 percent of the outstanding Units on an annual basis.



                                       4
<PAGE>   6

ITEM 2 -- MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND
          RESULTS OF OPERATIONS

RESULTS OF OPERATIONS

NET INCOME AND REVENUE

    The Partnership reported net income of $3 million in the first quarter of
2001, versus $1.6 million in the prior year period. Net income per Investing
Partner Unit increased 90 percent, from $1,072 per Unit to $2,036 per Unit.
Higher oil and natural gas prices during 2001 contributed to the increases in
net income and net income per Investing Partner Unit.

    Revenues increased 56 percent, from $2.6 million in the first quarter of
2000 to $4 million in the first quarter of 2001. Natural gas sales represented
81 percent of the Partnership's total revenues during the first quarter of 2001,
compared to 67 percent during the first quarter of 2000.

    The Partnership's oil and gas production volume and price information is
summarized in the following table (gas volumes presented in thousand cubic feet
(Mcf) per day):

<TABLE>
<CAPTION>
                                             FOR THE THREE MONTHS
                                                ENDED MARCH 31,
                                            --------------------       INCREASE
                                             2001           2000      (DECREASE)
                                            ------        ------      ----------
<S>                                         <C>           <C>            <C>
        Gas volume -- Mcf per day            4,862         7,471         (35%)
        Average gas price -- per Mcf        $ 7.45        $ 2.54         193%
        Oil volume -- barrels per day          288           322         (11%)
        Average oil price -- per barrel     $28.37        $27.63           3%
</TABLE>

FIRST QUARTER 2001 COMPARED TO FIRST QUARTER 2000

    Natural gas production revenues for the first quarter of 2001 totaled $3.3
million, 89 percent higher than the first quarter of 2000. Natural gas prices
for the first quarter of 2001 increased 193 percent compared to the year-earlier
period, which favorably impacted revenue by $3.3 million. Declines in the
Partnership's natural gas production offset $1.8 million of the favorable price
impact. Natural gas volumes on a daily basis decreased 35 percent from a year
ago due primarily to natural declines at Matagorda Island Block 681 and South
Timbalier 295. The lower gas volume in 2001 also reflects the Partnership taking
less than its entitled share of production at North Padre Island 969 to make-up
gas imbalances with another working interest owner.

    The Partnership's crude oil production revenues for the first quarter of
2001 totaled $.7 million, a nine percent decrease from the first quarter of
2000. The $74,000 decrease in oil sales was attributable to a 11 percent
decrease in daily oil production partially offset by a three percent increase in
oil prices.

    Given the small number of producing wells owned by the Partnership, and the
fact that offshore wells tend to decline at a faster rate than onshore wells,
the Partnership's future production will be subject to more volatility than
those companies with greater reserves and longer-lived properties. At December
31, 2000, South Timbalier Block 295 accounted for approximately 63 percent of
the Partnership's projected remaining equivalent proved reserves and 45 percent
of discounted future net cash flows relating to proved reserves.

OPERATING EXPENSES

    The Partnership's depreciation, depletion and amortization (DD&A) rate,
expressed as a percentage of oil and gas sales, was approximately 19 percent
during the first quarter of 2001 compared to 26 percent during the same period
in 2000. The decrease in the DD&A rate as a percentage of sales was primarily a
result of reserve additions and favorable reserve revisions recognized at the
end of 2000 and higher oil and gas prices.

    Lease operating expense (LOE) in the first quarter of 2001 decreased from
the first quarter of 2000 due to reduced repair and maintenance costs from a
year ago.


                                       5
<PAGE>   7

CASH FLOW, LIQUIDITY AND CAPITAL RESOURCES

CAPITAL RESOURCES AND LIQUIDITY

    The Partnership's primary capital resource is net cash provided by operating
activities, which was $3.5 million for the first three months of 2001. Net cash
provided by operating activities in 2001 was up 42 percent from a year ago due
to the increases in oil and gas prices. Future cash flows will be influenced by
fluctuations in product prices, production levels and operating costs.

CAPITAL COMMITMENTS

    The Partnership's primary needs for cash are for operating expenses,
drilling and recompletion expenditures, distributions to Investing Partners, and
the purchase of Units offered by Investing Partners under the right of
presentment.

    During the first three months of 2001, the Partnership's oil and gas
property additions totaled $.5 million. These additions related primarily to
participating in the A-13 sidetrack well being drilled at South Timbalier Block
295. Based on information supplied by the operators of the properties, the
Partnership anticipates capital expenditures of approximately $2.4 million for
the remainder of 2001, primarily for drilling and recompletions at South
Timbalier Block 295. Such estimates may change based on realized prices,
drilling results or changes by the operator to the development plan.

    The Partnership made distributions to Investing Partners of $2,000 per Unit
on March 1, 2001. The amount of future distributions will be dependent on actual
and expected production levels, realized and expected oil and gas prices,
expected drilling and recompletion expenditures, and prudent cash reserves for
future dismantlement and abandonment costs that will be incurred after the
Partnership's reserves are depleted.

    As provided in the Amended Partnership Agreement, a first right of
presentment offer for 2001 of $9,928 per Unit, plus interest to the date of
payment, was made to Investing Partners in April 2001, based on a valuation date
of December 31, 2000. The Partnership is not in a position to predict how many
Units will be presented for repurchase under the April 2001 offer and cannot, at
this time, determine if the Partnership will have sufficient funds available to
repurchase any Units. The Investing Partners have until May 23, 2001 to offer
their Units under the current right of presentment. The Partnership has no
obligation to purchase any Units presented to the extent it determines that it
has insufficient funds for such purchases. The Amended Partnership Agreement
contains limitations on the number of Units that the Partnership can repurchase,
including a limit of 10 percent of the outstanding Units on an annual basis.

FORWARD-LOOKING STATEMENTS AND RISK

    Certain statements in this report, including statements of the future plans,
objectives, and expected performance of the Partnership, are forward-looking
statements that are dependent on certain events, risks and uncertainties that
may be outside the Partnership's control, and which could cause actual results
to differ materially from those anticipated. Some of these include, but are not
limited to, the market prices of oil and gas, economic and competitive
conditions, inflation rates, legislative and regulatory changes, financial
market conditions, political and economic uncertainties of foreign governments,
future business decisions, and other uncertainties, all of which are difficult
to predict.

    There are numerous uncertainties inherent in estimating quantities of proved
oil and gas reserves and in projecting future rates of production and timing of
development expenditures. The total amount or timing of actual future production
may vary significantly from reserves and production estimates. The drilling of
exploratory wells can involve significant risks, including those related to
timing, success rates and cost overruns. Lease and rig availability, complex
geology and other factors can affect these risks. Fluctuations in oil and gas
prices, or a prolonged period of low prices, may substantially adversely affect
the Partnership's financial position, results of operations and cash flows.


                                       6
<PAGE>   8

COMMODITY RISK

    The Partnerships's major market risk exposure is in the pricing applicable
to its oil and gas production. Realized pricing is primarily driven by the
prevailing worldwide price for crude oil and spot prices applicable to its
natural gas production. Historically, prices received for oil and gas production
have been volatile and unpredictable and price volatility is expected to
continue. The Partnership did not use derivative financial instruments or
otherwise engage in hedging activities during 2000 or the first three months of
2001.






                                       7
<PAGE>   9

PART II -- OTHER INFORMATION


ITEM 1.    LEGAL PROCEEDINGS

           None.

ITEM 2.    CHANGES IN SECURITIES

           None.

ITEM 3.    DEFAULTS UPON SENIOR SECURITIES

           None.

ITEM 4.    SUBMISSION OF MATTERS TO A VOTE OF SECURITY HOLDERS

           None.

ITEM 5.    OTHER INFORMATION

           None.

ITEM 6.    EXHIBITS AND REPORTS ON FORM 8-K

           a.   Exhibits -- None.

           b.   Reports on Form 8-K -- None.





                                       8
<PAGE>   10

                                   SIGNATURES


Pursuant to the requirements of Section 13 or 15(d) of the Securities Exchange
Act of 1934, the registrant has duly caused this report to be signed on its
behalf by the undersigned thereunto duly authorized.


                                       APACHE OFFSHORE INVESTMENT PARTNERSHIP
                                       By: Apache Corporation, General Partner


Dated:   May 14, 2001                  /s/ Roger B. Plank
                                       ----------------------------------------
                                       Roger B. Plank
                                       Executive Vice President and
                                       Chief Financial Officer


Dated:   May 14, 2001                  /s/ Thomas L. Mitchell
                                       ----------------------------------------
                                       Thomas L. Mitchell
                                       Vice President and Controller
                                       (Chief Accounting Officer)