Gore, 35, was tackled awkwardly on a 10-yard run late in the first quarter. He struggled to get to the sideline with help from trainers and eventually was carted away.
After the game, he left the locker room with a walking boot on his left foot.
Dolphins coach Adam Gase did not have any further update on his status, but the source told Schefter later Sunday that an MRI had been scheduled to determine if Gore suffered any ligament damage. Gore does not have a fracture, the source added.
Gore is one of the NFL's most impressive iron men, having not missed a game since 2010. He's started 122 consecutive games, by far the longest stretch in the league. Tied for second are Christian McCaffrey and Peyton Barber with 17.
Rookie running back Kalen Ballage picked up the majority of Gore's workload Sunday after the veteran left the game. Ballage took the first snap of the second half 75 yards for a touchdown -- his first of the season.
Gase has leaned on Gore as a consistent and reliable lead back for the Dolphins (7-7). Gore needs 154 yards to tie Emmitt Smith for the most consecutive seasons with more than 1,000 scrimmage yards, at 13.
ESPN NFL Insider Adam Schefter contributed to this report.