ESPN's Adam Schefter and the NFL Network's Ian Rapoport both reported Bennett is dealing with the injury.
The Patriots claimed Bennett off waivers on Thursday, one day after he was waived by the Green Bay Packers with the designation that he failed to disclose a physical condition.
The 30-year-old Bennett passed his physical with the Patriots on Friday and was on the practice field, rejoining the team with which he won a Super Bowl ring last season.
Bennett, playing in his 10th NFL season, had just 24 receptions in seven games with the Packers but had not played since Oct. 22 -- the week before Green Bay's bye week. He was inactive for Monday night's loss to Detroit after being listed with a shoulder injury last week.
During the bye week, Bennett posted on Instagram that he was "pretty sure" he would retire at the end of the 2017 season.
Signed to a three-year, $21 million contract in the offseason, the 6-foot-6, 275-pound Bennett failed to find the end zone with Green Bay, but he appeared in all 16 games with New England last season, hauling in 55 catches and scoring a career-high seven touchdowns.
Packers coach Mike McCarthy said Friday that surgery was being discussed before the Packers released Bennett.
"I'm not going to get into the Patriots claiming Marty, I'll just reiterate what I said yesterday: I just know what the facts are and how the timeline came about," McCarthy said, according to ESPN. "I talked to him Tuesday (following the bye week) after practice and he (had) a shoulder concern injury. I advised him to get the second opinions. He did that and he went to a number of them. The last medical conversation I was involved with in regards to Marty, they were talking about scheduling surgery. After that, then you have the termination and then the claim. I really don't have any comments on that. I've answered the question for the last time, respectfully."
Bennett disputed the Packers' reason for his release on Friday afternoon in an Instagram post.
"The packers examined my shoulder on my visit March 10 and cleared it," Bennett said in part on Instagram. "They even gave me an xray as well. It got worse during the season, specifically against the Cowboys so I asked to have it checked out and we checked it. After a few days of contemplating to play with it or get surgery, I chose surgery. Now here we are. ..."