The operation, to repair a tear in his left hip, was slated to take place in Vail, Colo. Rozsival is expected to make a full recovery in four to six weeks.
The 29-year-old Rozsival recently completed a two-year deal worth $4.2 million, including $2.3 last season -- when he scored a career-high 13 goals and added 25 assists in 80 games.
The native of the Czech Republic has played three seasons with New York after a four-season stint with the Pittsburgh Penguins. He has 46 goals and 173 points in 479 regular-season NHL games.
Rozsival notched a goal and five assists in the Rangers' 10 postseason games this year.