The forward was described as day to day by Rangers coach Gerard Gallant on Jan. 22 when he skated in warmups but did not play in a 7-3 win against the Arizona Coyotes. Kakko has missed six games.
"The trainer told me this morning it's going to be a month," Gallant said. "We want to make sure he's ready to go. We'll see where he is in three weeks' time."
Gallant didn't say if Kakko had or will need surgery but said the injury was bothering him for a week or two before the game against Arizona.
Kakko scored 14 points (five goals, nine assists) in 37 games. He was playing regularly in the top six forwards, most recently on a line with center Mika Zibanejad and left wing Chris Kreider.
Kreider is tied for the NHL lead with 33 goals (Leon Draisaittl, Edmonton Oilers) and has scored 47 points in 47 games. Zibanejad has scored 49 points (18 goals, 31 assists) in 47 games.
"[Kakko] was playing fine," Gallant said. "Kakko is a real good defensive player. He wasn't scoring as much as he likes, but I liked his game. He's an intelligent player for a young player (20). I liked his game. He played a lot with the top lines and he's trending in the right direction. There's nothing I haven't liked about Kaapo all year. He'd just like to score more and we'd liked to see him score a little bit more, but we liked his game."
Defenseman Adam Fox returned to practice Friday after missing three games before the All-Star break because of an upper-body injury sustained Jan. 27 in a 5-3 loss at the Columbus Blue Jackets.
He is expected to return to play at the Boston Bruins on Tuesday. The Rangers have not played since Feb. 1, when they defeated the Florida Panthers 5-2.
"He looks good out there," Gallant said of Fox. "I mean, first day, but he looks good, everything is going good and we expect him to be ready to play."
Fox, who was removed from injured reserve Wednesday, is tied with Victor Hedman of the Tampa Bay Lightning for first among NHL defenseman with 47 points (seven goals, 40 assists) in 44 games.
Filip Chytil also practiced Friday and Gallant said he could play against the Bruins after missing five games with a lower-body injury. The forward has scored 11 points (four goals, seven assists) in 38 games.
"He skated really good today and we'll take it one day at a time," Gallant said. "I see him being real close if he's not ready now."