The 31-year old USA international scored the match-winning goal as well as providing an assist as the Dynamo beat Chicago Fire 2-1 on the weekend.
Davis netted the winner in the 81st minute with a cross which evaded all in the box and found its way into the Fire goal after supplying Will Bruin with the opener in the 26th minute.
Davis becomes the first Houston player to win the weekly prize in the 2013 season.
2013 MLS Player of the Week
Week 7: Brad Davis (Houston Dynamo) Week 6: Ryan Johnson (Portland Timbers) Week 5: Will Johnson (Portland Timbers) Week 4: Juan Agudelo (Chivas USA) Week 3: Bill Hamid (DC United) Week 2: Robert Earnshaw (Toronto FC) Week 1: Mike Magee (LA Galaxy)