The man, whose name wasn't immediately released, entered Bemer Plus about 4 pm and officers received a call minutes later about "a shooting in progress," Executive Assistant Police Chief Troy Finner said in a news conference.
Multiple people, including customers and other employees, were at the shop when the shooting happened, Finner said.
"It's very, very sad this time of year and any part of the year that we lose three citizens," Finner said. "I just ask our great citizens of this city to pray for each victim here and their families."
The southwest Houston shop specialises in used BMW sales and repairs.
Hours after the shooting, homicide detectives were still at the scene investigating.
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