Garrett could return to the Browns as early as next week against the Los Angeles Chargers, but he is expected to feel the effects of the shoulder injury for up to a month, the source said.
Garrett has been diagnosed with a sprained AC joint in his left shoulder and a right biceps strain after the crash Monday, when police said his 2021 Porsche left the road, struck a ditch and hit a fire hydrant before flipping over several times.
The shoulder sprain is considered the more significant of the two injuries, the source said, although the biceps strain also could affect Garrett for multiple weeks.
Garrett has been ruled out of Sunday's game against the Atlanta Falcons after initially being listed as questionable. The three-time Pro Bowler was released from an Akron, Ohio, hospital Monday night and has cleared the concussion protocol, according to the Browns.
Garrett, 26, also suffered cuts and bruises and told reporters Friday that he popped a blood vessel in his left eye, which was still visibly red. He said he was "definitely grateful" to be alive and that he was "recovering pretty quickly" from injuries.
"Definitely grateful to be here," Garrett said. "With what I saw right after ... the pictures, it was a helluva event."
Garrett crashed his car near Wadsworth, Ohio, according to the Ohio State Highway Patrol, which reiterated that impairment by drugs or alcohol is not suspected. A female passenger who was in the vehicle also was taken to the hospital with what were described as minor injuries. Garrett and the woman both were wearing seat belts.