**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, a series of DWS Money Market Trust, on Form N-CSR; |
|----|-----------------------------------------------------------------------------------------------------------------------------|

 

| 2. | Based on my knowledge and pursuant to 18 U.S.C. § 1350, the periodic report on Form N-CSR (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. |
|----|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|

 

 

 

| March 2, 2009 | /s/Michael G. Clark                                         |
|---------------|-------------------------------------------------------------|
|          | Michael G. Clark                                            |
|          | President                                                   |
|          | DWS Money Market Series, 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, a series of DWS Money Market Trust, on Form N-CSR; |
|----|-----------------------------------------------------------------------------------------------------------------------------|

 

| 2. | Based on my knowledge and pursuant to 18 U.S.C. § 1350, the periodic report on Form N-CSR (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. |
|----|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|

 

 

| March 2, 2009 | /s/Paul Schubert                                            |
|---------------|-------------------------------------------------------------|
|          | Paul Schubert                                               |
|          | Chief Financial Officer and Treasurer                       |
|          | DWS Money Market Series, a series of DWS Money Market Trust |