Citing two sources, Rapoport said Hernandez likely will be ready by training camp. It is unclear when the injury occurred.
Last week, Hernandez said his goal for the upcoming season was to get through 16 games for the first time in his NFL career.
The news of Hernandez's surgery, coupled with Rob Gronkowski's injury complications, makes the Patriots' depth chart look a little less prolific with Daniel Fells, Jake Ballard, Brad Herman and Michael Hoomanawanui -- who the Pats re-signed Tuesday -- the remaining tight ends on the roster.
While Gronk's injury and the lack of an outside receiving threat are issues, as long as Hernandez is back in the fold in time to knock the rust off with Brady before the season starts, Hernandez's injured shoulder shouldn't be a huge concern.
Follow Kevin Patra on Twitter @kpatra.