The forward, who was injured in a 4-2 loss at the Buffalo Sabres on Monday, was placed on injured reserve.
Stastny will sit out the remainder of the five-game road trip -- at the Pittsburgh Penguins on Thursday, and at the Philadelphia Flyers on Saturday -- and be re-evaluated when the Golden Knights return to Las Vegas.
"He's going to be a little longer term than we thought," coach Gerard Gallant said before the game Wednesday. "He's not going to play the next three games and then we'll know more next week when we get home."
Tomas Nosek moved into Stastny's spot at center on the second line, and center Cody Eakin made his season debut after missing the first three games with a lower-body injury.
Stastny did not have a point in the first three games after signing as an unrestricted free agent July 1.
Stastny had 53 points (16 goals, 37 assists) in 82 games last season with the St. Louis Blues and the Winnipeg Jets. He had 15 points (six goals, nine assists) in 17 Stanley Cup Playoff games with Winnipeg.
