Morrow will be evaluated in a week but the team said the typical recovery time is four to six weeks. The injury occurred during practice.
The Thunder signed Morrow to a three-year, $10 million contract in July. The 29-year-old spent last season with the New Orleans Pelicans. He averaged 8.4 points and 1.8 rebounds as a reserve, while shooting 45.1 percent from the three-point line.
Oklahoma City has already lost forwards Kevin Durant and Mitch McGary for the start of the season. Durant, the league's reigning MVP, sustained a fracture in his foot on Oct. 11 and rookie McGary broke his foot on Oct. 8. Both are expected to miss at least the first month of the season.
Thunder guard Reggie Jackson is currently dealing with a bruised wrist but is expected to play in the team's opener.
Oklahoma City opens the regular season Wednesday against the Portland Trail Blazers.
- Molly Geary