The 20-year old winger netted twice as his side defeated San Jose Earthquakes 2-0 at Pizza Hut Park on the weekend.
His first goal came in the 58th minute when he finished neatly from a David Ferreira pass before flicking a long ball past Quakes keeper Joe Cannon two minutes later.
It was the first time in his career that Shea had scored more than once and was the first a Dallas player has been awarded this season.
2010 MLS Player of the Week awards
Week 1: Javier Morales (Real Salt Lake)
Week 2: Kenny Mansally (New England Revolution)
Week 3: Sebastien Le Toux (Seattle Sounders)
Week 4: Edson Buddle (LA Galaxy)
Week 5: Dwayne De Rosario (Toronto FC)
Week 6: Edson Buddle (LA Galaxy)
Week 7: Landon Donovan (LA Galaxy)
Week 8: Alvaro Saborio (Real Salt Lake)
Week 9: Emilio Renteria (Columbus Crew)
Week 10: Dwayne De Rosario (Toronto FC)
Week 11: Brek Shea (FC Dallas)