Free likely would have needed surgery had there been significant ligament damage, but instead he'll be in a walking boot.
Cowboys owner and general manager Jerry Jones said Tuesday there is some hope Free could return sooner because he does not play a skill position.
Jermey Parnell will replace Free in the starting lineup.
"Got a lot of confidence in him," Jones said Tuesday of Parnell on 105.3 The Fan. "We really do, although I don't want to take anything away from Doug Free. His leadership ... he's the daddy in that offensive line room, and he's also playing very well this year. But Parnell is capable of coming in and playing well, too. He's got a lot of talent. He's just got to not make mistakes."
Parnell is dealing with a rib injury that limited his work in practice last week. Donald Hawkins, who has been inactive the first six games, would take over as the backup tackle in Free's absence.
Jones said the Cowboys do not want to move right guard Zack Martin to tackle. Martin played left tackle at Notre Dame but has not worked at tackle since the Cowboys drafted him in the first round.
Jones all but ruled out making any trade or adding a player from another team's practice squad. The Cowboys have tackle John Wetzel on their practice squad.
"Right now, Parnell is our answer," Jones said, "and a good one."