"Nothing has stopped him from playing, but under the current circumstances he will be given rest to avoid aggravating it, and he can begin his leave," New Jersey coach Sheldon Keefe told the club's website.
New Jersey will miss the playoffs and has three regular-season games remaining.
The 36-year-old goalkeeper played the last three Olympic matches with Tre Kronor, who lost to gold-winning USA in the quarterfinals after extra time.
With New Jersey's announcement, it is doubtful Markström will be available for the World Championships in Switzerland from May 15-31.
