"I'm sure we've had other guys in that situation, so we're guessing four to six weeks," Munchak said. "Every guy is different, heals differently, but I'm sure it's going to be somewhere in that time frame."
Hope was hurt early in the Titans' 31-13 win at Cleveland on Sunday, his first start after missing two games with a shoulder he dislocated in the season opener.
Jordan Babineaux replaced Hope and returned a Colt McCoy interception 97 yards for a touchdown.
Munchak said Hope will have surgery this week. A 10-year veteran, Hope is in the final year of his contract and earning $6.5 million.
Tight end Craig Stevens likely will be limited with a rib injury, and starting left guard Leroy Harris will be limited after getting a knee and ankle caught up in a pile.
The Associated Press contributed to this report.