The third-year forward has a sprained left ankle and is expected to miss three weeks, the team said Wednesday.
Wright is expected to spend one week in a cast and the following two weeks rehabbing.
Wright said he wasn't sure when the injury occurred but noticed the ankle started swelling about three hours after the Heat beat the New Orleans Hornets 109-105 in an exhibition game Tuesday night. Wright started that game and finished with 13 points and 10 rebounds, earning praise from coach Pat Riley.
The Heat have four preseason games left before opening the regular season at home against Chicago on Oct. 31.