Hill suffered a torn ACL on Sunday and is out for the season, Ian Rapoport of NFL Network reported Monday.
Hill, 25, signed with the Patriots this season after spending four years with the Cincinnati Bengals.
The Patriots edged the Houston Texans 27-20 in their opener, but Hill left the game with a knee injury after rushing for 25 yards on four carries and catching one pass for six yards.
The Patriots signed Hill in the offseason and drafted running back Sony Michel in the first round. However, Michel missed the opener with an injury, and now Hill is out.
Rex Burkhead was the Patriots' leading rusher on Sunday with 18 carries for 64 yards. James White had five carries for 18 yards, and wide receiver Cordarrelle Patterson ran the ball three times for 13 yards.
Last season, Hill started all seven games in which he appeared for the Bengals and rushed for just 116 yards while making four receptions for 16 yards.
He rushed for 839 yards in 2016, and his best season was his rookie year when he rushed for 1,124 yards in 16 games, including eight starts.