<PAGE>   1

                       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, 2000

                                       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,
                                                -------------------------
                                                   2000           1999
                                                ----------     ----------
<S>                                             <C>            <C>
REVENUES:
   Oil and gas production revenues              $2,534,975     $1,663,778
   Interest income                                  36,682         16,350
                                                ----------     ----------
                                                 2,571,657      1,680,128
                                                ----------     ----------
EXPENSES:
   Depreciation, depletion and amortization        659,037        673,620
   Lease operating expense                         143,606        153,865
   Administrative                                  135,000        135,000
                                                ----------     ----------
                                                   937,643        962,485
                                                ----------     ----------
NET INCOME                                      $1,634,014     $  717,643
                                                ==========     ==========
NET INCOME ALLOCATED TO:
   Managing Partner                             $  420,180     $  231,761
   Investing Partners                            1,213,834        485,882
                                                ----------     ----------
                                                $1,634,014     $  717,643
                                                ==========     ==========
NET INCOME PER INVESTING PARTNER UNIT           $    1,072     $      426
                                                ==========     ==========

WEIGHTED AVERAGE INVESTING PARTNER
   UNITS OUTSTANDING                               1,132.5        1,141.0
                                                ==========     ==========
</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,
                                                                           ----------------------------
                                                                              2000             1999
                                                                           -----------      -----------
<S>                                                                        <C>              <C>
CASH FLOWS FROM OPERATING ACTIVITIES:
   Net income                                                              $ 1,634,014      $   717,643
   Adjustments to reconcile net income to net cash
      provided by operating activities:
         Depreciation, depletion and amortization                              659,037          673,620
         Changes in operating assets and liabilities:
             Decrease in accrued revenues receivable                             3,293          289,878
             (Decrease) increase in accrued operating expenses payable         (55,014)           2,407
             Increase (decrease) in receivable from/payable to
                 Apache Corporation                                            243,123         (195,069)
                                                                           -----------      -----------
         Net cash provided by operating activities                           2,484,453        1,488,479
                                                                           -----------      -----------
CASH FLOWS FROM INVESTING ACTIVITIES:
   Additions to oil and gas properties                                        (724,462)        (504,293)
   Non-cash portion of oil and gas property additions                         (131,747)         125,490
                                                                           -----------      -----------
         Net cash used in investing activities                                (856,209)        (378,803)
                                                                           -----------      -----------
CASH FLOWS FROM FINANCING ACTIVITIES:
   Distributions to Investing Partners                                      (2,264,978)        (855,728)
   Distributions to Managing Partner, net                                     (404,243)        (331,326)
                                                                           -----------      -----------
         Net cash used in financing activities                              (2,669,221)      (1,187,054)
                                                                           -----------      -----------
NET DECREASE IN CASH AND CASH EQUIVALENTS                                   (1,040,977)         (77,378)
CASH AND CASH EQUIVALENTS, BEGINNING OF YEAR                                 2,748,812        1,324,949
                                                                           -----------      -----------
CASH AND CASH EQUIVALENTS, END OF PERIOD                                   $ 1,707,835      $ 1,247,571
                                                                           ===========      ===========
</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,
                                                                        2000              1999
                                                                   -------------      -------------
                                  ASSETS
<S>                                                                <C>                <C>
CURRENT ASSETS:
   Cash and cash equivalents                                       $   1,707,835      $   2,748,812
   Accrued revenues receivable                                           632,533            635,826
                                                                   -------------      -------------
                                                                       2,340,368          3,384,638
                                                                   -------------      -------------
OIL AND GAS PROPERTIES, on the basis of full cost accounting:
   Proved properties                                                 170,220,808        169,496,346
   Less - Accumulated depreciation, depletion and amortization      (164,817,605)      (164,158,568)
                                                                   -------------      -------------
                                                                       5,403,203          5,337,778
                                                                   -------------      -------------
                                                                   $   7,743,571      $   8,722,416
                                                                   =============      =============
                    LIABILITIES AND PARTNERS' CAPITAL

CURRENT LIABILITIES:
   Accrued exploration and development                             $     465,104      $     596,851
   Accrued operating expenses payable and other                          117,057            172,071
   Payable to Apache Corporation                                         441,754            198,631
                                                                   -------------      -------------
                                                                       1,023,915            967,553
                                                                   -------------      -------------
PARTNERS' CAPITAL:
   Managing Partner                                                      254,016            238,079
   Investing Partners (1,132.5 units outstanding)                      6,465,640          7,516,784
                                                                   -------------      -------------
                                                                       6,719,656          7,754,863
                                                                   -------------      -------------
                                                                   $   7,743,571      $   8,722,416
                                                                   =============      =============
</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.   RECEIVABLE FROM/PAYABLE TO APACHE CORPORATION

     Receivable from/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 from/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 2000 is expected
to be made to Investing Partners in May, based on a valuation date of December
31, 1999. The Partnership is not in a position to predict how many Units will
be presented for repurchase under the May 2000 offer and cannot, at this time,
determine if the Partnership will have sufficient funds available to repurchase
all Units presented. 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 $1.6 million in the first quarter
of 2000, versus $.7 million in the prior year period. Net income per Investing
Partner Unit increased 152 percent, from $426 per Unit to $1,072 per Unit.
Higher oil and natural gas prices during 2000 contributed to the increases in
net income and net income per Investing Partner Unit.

     Revenues increased 53 percent, from $1.7 million in the first quarter of
1999 to $2.6 million in the first quarter of 2000. Natural gas sales
represented 67 percent of the Partnership's total revenues during the first
quarter of 2000, compared to 80 percent during the first quarter of 1999.

     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
                                     2000          1999         (DECREASE)
                                   ---------     ---------      ---------

<S>                                <C>           <C>            <C>
Gas volume - Mcf per day               7,471         9,241            (19%)
Average gas price - per Mcf        $    2.54     $    1.62             57%
Oil volume - barrels per day             322           317              2%
Average oil price - per barrel     $   27.63     $   11.17            147%
</TABLE>



FIRST QUARTER 2000 COMPARED TO FIRST QUARTER 1999

     Natural gas production revenues for the first quarter of 2000 totaled $1.7
million, 29 percent higher than the first quarter of 1999. Natural gas prices
increased 57 percent for the first quarter of 2000 compared to the year-earlier
period, which favorably impacted revenue by $.8 million. Natural gas volumes on
a daily basis decreased 19 percent from a year ago due to natural declines at
Matagorda Island Block 681 and the sale of the Partnership's interest in
Matagorda Island Block 705 during 1999.

     The Partnership's crude oil production revenues for the first quarter of
2000 totaled $.8 million, a 154 percent increase from the first quarter of
1999. The $.5 million increase in oil sales was attributable to a 147 percent
increase in the average realized oil price and a two percent increase in daily
oil production.


OPERATING EXPENSES

     The Partnership's depreciation, depletion and amortization (DD&A) rate,
expressed as a percentage of oil and gas production revenues, was approximately
26 percent during the first quarter of 2000 compared to 40 percent during the
same period in 1999. The decrease in the DD&A rate was primarily a result of
upward reserve revisions recognized at the end of 1999.

     Lease operating expense (LOE) in the first quarter of 2000 decreased from
the first quarter of 1999 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 $2.5 million for the first three months of
2000. Net cash provided by operating activities in 2000 was up 67 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 2000, the Partnership's oil and gas
property additions totaled $.7 million. These additions related primarily to
participating in the A-31 development 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 $1.0 million
for the remainder of 2000, 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, 2000. 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 right of presentment
offer for 2000 is expected to be made to Investing Partners in May, based on a
valuation date of December 31, 1999. The Partnership is not in a position to
predict how many Units will be presented for repurchase under the May 2000
offer and cannot, at this time, determine if the Partnership will have
sufficient funds available to repurchase any Units. 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 control of the Partnership or the
Managing Partner and which could cause actual results to differ materially from
those anticipated. Some of these include, but are not limited to, 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. Future oil and gas
prices also could affect results of operations and cash flows.


                                       6
<PAGE>   8

                          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.

                  27.1         Financial Data Schedule.

             b.   Reports on Form 8-K - None.




                                       7
<PAGE>   9


                                   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 11, 2000                /s/ Roger B. Plank
                                      ------------------------------------------
                                      Roger B. Plank
                                      Vice President and Chief Financial Officer


Dated:    May 11, 2000                /s/ Thomas L. Mitchell
                                      ------------------------------------------
                                      Thomas L. Mitchell
                                      Vice President and Controller
                                      (Chief Accounting Officer)

<PAGE>   10

                                 EXHIBIT INDEX

<TABLE>
<CAPTION>

EXHIBIT NO.       DESCRIPTION
-----------       -----------
<S>         <C>   <C>
27.1         -    Financial Data Schedule
</TABLE>