**President**

**Section 906 Certification under Sarbanes Oxley Act**

 

 

 

I, Michael G. Clark, certify that: 

 

| 1. | I have reviewed this report, filed on behalf of DWS Money Market Series (Institutional), a series of DWS Money Market Trust, on Form N-CSRS; |
|----|----------------------------------------------------------------------------------------------------------------------------------------------|

 

| 2. | Based on my knowledge and pursuant to 18 U.S.C. § 1350, the periodic report on Form N-CSRS (the “Report”) fully complies with the requirements of § 13 (a) or §15 (d), as applicable, of the Securities Exchange Act of 1934 and that the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company. |
|----|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|

 

 

 

| August 26, 2008 | /s/Michael G. Clark                                                         |
|-----------------|-----------------------------------------------------------------------------|
|            | Michael G. Clark                                                            |
|            | President                                                                   |
|            | DWS Money Market Series (Institutional), a series of DWS Money Market Trust |

 

 

 

 

**Chief Financial Officer and Treasurer**

**Section 906 Certification under Sarbanes Oxley Act**

 

 

 

I, Paul Schubert, certify that: 

 

| 1. | I have reviewed this report, filed on behalf of DWS Money Market Series (Institutional), a series of DWS Money Market Trust, on Form N-CSRS; |
|----|----------------------------------------------------------------------------------------------------------------------------------------------|

 

| 2. | Based on my knowledge and pursuant to 18 U.S.C. § 1350, the periodic report on Form N-CSRS (the “Report”) fully complies with the requirements of § 13 (a) or § 15 (d), as applicable, of the Securities Exchange Act of 1934 and that the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company. |
|----|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|

 

 

| August 26, 2008 | /s/Paul Schubert                                                            |
|-----------------|-----------------------------------------------------------------------------|
|            | Paul Schubert                                                               |
|            | Chief Financial Officer and Treasurer                                       |
|            | DWS Money Market Series (Institutional), a series of DWS Money Market Trust |