Jets coach Scott Arniel told reporters after Vegas' 4-3 overtime win that Fleury would stay in hospital overnight.
Winnipeg's bench emptied onto the ice in a show of support for Fleury as he was taken off the ice.
After the game resumed, Winnipeg's Adam Lowry fought Kolesar.
Fleury, a 29-year-old Canadian, is in his second season with the Jets. He previously played for Tampa Bay, Seattle, Anaheim and Carolina. Fleury has 10 career goals and 44 points.
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