Foster played in the first half before suffering the injury. He had three carries for 9 yards. He was ruled out at the start of the third quarter.
After the game, Dolphins coach Adam Gase said the team would know more about Foster's injury on Monday.
The four-time Pro Bowl running back has a long history of injuries, including last year's season-ending Achilles injury. Foster, 30, also entered Sunday's game with a hamstring injury.
Miami backup running backs Jay Ajayi and rookie Kenyan Drake got most of the work in place of Foster. Drake rushed for 12 yards on two carries, including a 7-yard touchdown run. Ajayi finished with 14 yards on five carries.
"It is the next-man-up mentality. Whoever is on the field is going to play. You just have to play to the best of your ability," Ajayi said.
Quarterback Ryan Tannehill led the Dolphins in rushing, gaining 35 yards on six carries in Miami's 31-24 loss to the Patriots.
Ajayi had a costly fumble in the third quarter, when the Dolphins were driving into Patriots territory, down 21 points at the time.
"I've just got to hold onto the ball," Ajayi told reporters. "It was a costly mistake."
ESPN's Chris Forsberg contributed to this report.