"I spoke with our medical guys and [Jagr] and it's coming real, real good," Gulutzan said. "We think it'll probably be about a week and he should be back."
Jagr was injured during the first period of a 4-2 loss against the Minnesota Wild on Saturday.
He has two assists in five games since signing a one-year, $1 million contract with the Flames on Oct. 4, and had been playing on the top line with Johnny Gaudreau and Sean Monahan at the time of the injury.
"I thought we were doing some good things," Gaudreau said. "I think he's a really skilled player. I really liked playing with him the first few games there. I thought we did some good things. It was short, but back to a rotation."
Jagr, 45, didn't have an NHL training camp to prepare him for the season, but Gulutzan wasn't sure his quick ramp-up to NHL speed played a factor in the injury.
"For me, he was right where he was needing to be," Gulutzan said. "He just felt that he was feeling good now with his conditioning and his timing and all that. I think he was in a real good spot.
"All I know is you look at his career, he hasn't been out too, too much. Maybe that has something to do with it. He pushed himself real hard to get up and ready. But it's good. We've got a guy that's played a lot of games in the League and he kind of knows where he's at.
"He's in a better spot because he knows his body and knew when to get himself out."
Jagr is fourth all-time in NHL games played with 1,716, and needs to play 51 more to tie Gordie Howe's record of 1,767. He is third with 765 NHL goals, behind Wayne Gretzky (894) and Howe (801), and is second in points with 1,916, behind Gretzky (2,857).
"A lot of experience," Gaudreau said. "You can learn from him every day and watch him in practice and pick his brain. It's great to have him around our locker room. He's helping our team on the ice and he's helping us be better players off the ice as well. Learning from him, it's been great so far."
The Flames recalled forward Mark Jankowski from Stockton of the American Hockey League on Monday. He has eight points (five goals, three assists) in six games. The No. 21 pick of the 2012 NHL Draft, Jankowski made his NHL debut last season.
Calgary next plays at the Nashville Predators on Tuesday (8 p.m. ET; FS-TN, SNF, NHL.TV).
