Achane is expected to miss the minimum four games and return after the Dolphins' bye for their Week 11 game against the Las Vegas Raiders, the source said.
Dolphins cornerback Jalen Ramsey, who had knee surgery in July, is ahead of schedule in his comeback and pushing to play sometime next month, league sources told Schefter.
"He's tracking well and wants to come back sooner rather than later," one source said.
While the Dolphins don't know when Ramsey will be available to return, the game vs. the Raiders on Nov. 19 could be a target, allowing him to play the final eight games of the season.
Achane enters Sunday as the NFL's second-leading rusher with 460 yards on just 38 carries. He was placed on injured reserve Wednesday with a knee injury, although Dolphins coach Mike McDaniel acknowledged the roster move was not a "black and white" decision.
The Dolphins opened the window last week for Jeff Wilson Jr. to return from IR, but the veteran running back will not play against Carolina.