The New York Daily News and New York Post both reported that Nash, 28, suffered a bruised shoulder while playing for Davos on Friday.
It is not known exactly how much time Nash will miss. The right wing is expected to be re-evaluated this week as he competes in Switzerland with the NHL lockout ongoing. He also played for Davos during the 2004-05 lockout.
Nash was traded to the New York Rangers in July from Columbus along with a conditional 2013 third-round draft pick and minor-league defenceman Steve Delisle. In return, the Rangers sent centres Brandon Dubinsky and Artem Anisimov, defenceman Tim Erixon and a first-round pick in 2013.
He scored 289 goals and 259 assists in 674 regular season games over nine seasons with the Blue Jackets, where he was the face of the franchise.