Nash played several more shifts after the hit but then left the game and didn't return for the second period of the Rangers' 9-2 loss to the Sharks.
Nash has a history of concussions, but there was no immediate word on his condition and whether he might be sidelined.
Stuart received a minor penalty for elbowing at 2:23 of the first period. Replays appeared to show Stuart's shoulder hitting Nash's head.
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The NHL fined New York Islanders forward Frans Nielsen $5,000.
Nielsen was fined by the NHL's Department of Player Safety for slashing visiting Phoenix Coyotes forward Martin Hanzal during a game on Tuesday.
The penalty occurred at 13:42 of the third period. Nielsen was assessed a minor penalty for his actions, as well.
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Tampa Bay Lightning center Tom Pyatt is out indefinitely after breaking a collarbone in his first game of the season on Tuesday night.
Pyatt suffered the injury in the third period of the Lightning's 3-2 overtime victory over the Buffalo Sabres. He had missed Tampa Bay's first two games this season with an upper body injury.
The 26-year-old Pyatt, who is considered a defensive forward, had eight goals and eight assists in the lockout-shortened 2013 season and 12 goals and seven assists in 74 games during the 2011-12 season.