The rookie defensive end received medical attention after throwing a punch at center Joe Hawley during pass-rush drills on Sunday.
An initial ESPN.com report stated that Hageman suffered what was believed to be a hairline fracture in the wrist. NFL Media Insider Ian Rapoport reported Hageman suffered no broken bones, according to a source with direct knowledge of the situation.
"I think we're all talking about competing and fighting for jobs, but we're not talking about fighting each other," coach Mike Smith said. "We've got to understand that."
Also Sunday, offensive lineman Terren Jones suffered an apparent neck injury during a drill. Jones was put on a backboard and had his neck immobilized before being carted off the field and transported to a local hospital.
The extent of his injury is unknown at this time.
"We certainly hope Terren will be all right," Smith said. "We don't have any update right now, but as soon as we do, we will release that information. Any time a player doesn't leave the field on his own power, you are always concerned."
Jones spent last season on the practice squad and has been in competition for a reserve role.