Vereen suffered the injury early in Sunday's season-opening victory over the Buffalo Bills, according to the report, but played the entire game. Vereen did not practice Monday, according to the team's practice report.
After New England's 23-21 win, Vereen experienced numbness because the bone sits on a nerve, according to the report.
Vereen rushed for a career-high 101 yards and had seven receptions for 58 yards Sunday. The third-year veteran filled in as New England's primary running back after starter Stevan Ridley was benched following a second-quarter fumble.
Elsewhere, receiver Danny Amendola was listed as limited with a groin injury. He left Sunday's game late in the second quarter but returned in the second half.
Also, running back Brandon Bolden (knee), receiver Aaron Dobson (hamstring), safety Nate Ebner (ankle), tight end Rob Gronkowski (back/forearm), safety Duron Harmon (hamstring), tight end Zach Sudfeld (hamstring), offensive lineman Will Svitek (knee) and running back Leon Washington (thigh) were listed as limited.
Gronkowski, recovering from surgeries on his arm and back, is unlikely to see action against the Jets on Thursday, league sources tell ESPN NFL Insider Adam Schefter. Gronkowski probably won't see his first action until Week 3, when the Patriots face the Buccaneers at home.
Sudfeld was limited to four snaps in the second half Sunday, three of which came on the Patriots' final possession.