The 29-year-old defenseman left after taking a check from Lightning forward J.T. Miller. He had his left arm in a sling after the game.
"It's a blow to us," Rangers coach David Quinn said Wednesday. "He's been playing well, but we got eight D we feel comfortable with night in and night out."
Signed by the Rangers to a four-year contract July 1, 2017, Shattenkirk has eight points (one goal, seven assists) in 29 games this season. He missed the final 36 games last season because of a meniscus tear in his left knee.
Quinn is hoping forwards Mats Zuccarello (groin), Pavel Buchnevich (broken thumb), and defenseman Adam McQuaid (lower body), will return when Rangers (14-13-3) play the Arizona Coyotes at Madison Square Garden on Friday (7 p.m. ET; MSG 2, FS-A, NHL.TV). Forwards Steven Fogarty and Cole Schneider were assigned to Hartford of the American Hockey League on Tuesday, a sign the Rangers could get back at least one of their injured forwards.
"He's worked really hard coming back," Quinn said of Zuccarello, who has missed seven games since Nov. 23. "I know he wants to come back. He's been wanting to come back for a while, but it just didn't make sense to put him in a situation where he was going to be in and out. We want to make sure when he comes back it's full go and there's no holding back."
The Rangers are also without forward Cody McLeod (fractured hand) and the injuries have taken their toll. New York is 2-5-1 since a 9-1-1 stretch from Oct. 30 to Nov. 2 and are fifth in the Metropolitan Division.
"We've missed all of them, for sure," Quinn said. "But every team has injuries and you have to overcome them and have to deal with them. It's just the reality of the National Hockey League."
Like Zuccarello and Buchnevich, McQuaid, out since Oct. 25, practiced in a regular jersey.
"The timing is perfect obviously with [Shattenkirk] going down and having Adam come back and the ability to go full go," Quinn said. "It was good timing from an injury perspective."