Wright got hurt during 7-on-7 drills about halfway through the Browns' morning workout Tuesday. He was attended to on the sideline by trainers, who put an ice wrap on Wright's leg. He limped to the team's training facility for further treatment.
Wright's injury appeared to be to his hamstring. It's not yet known if it will keep him out of Saturday's exhibition opener against Green Bay.
Before the evening practice session, Wright walked onto the field without a limp but did not have his helmet. He worked out on a hand bike as his teammates warmed up nearby.
A second-round pick in 2007, Wright had four interceptions last season. If he is out for any extended period, rookie Joe Haden would likely take his spot.
Haden received all of the first-team reps Tuesday after Wright went down. Haden's learning curve will increase even more if he starts Saturday's preseason opener against the Green Bay Packers, who should have one of the NFL's top offenses this year.
"I'm real excited," Haden said of the potential opportunity. "It definitely means a whole lot more playing time, and that's just more time to make plays."
The news wasn't all good for Haden this week.
Cleveland players have made headlines recently with their Twitter accounts. Haden added to the list by recently tweeting that a teammate was fined for a cell phone going off in a team meeting. Browns head coach Eric Mangini was disappointed because he had just warned the team on Monday about using social networking irresponsibly.
"I wasn't trying to tell everybody our business, but I really need to make sure I don't reveal what's going on inside the locker room," Haden said. "I apologized and [Mangini] said we're going to move on."
Added Mangini: "I think our social media policy is a work in progress."
Information from The Associated Press and ESPN.com's James Walker was used in this report.