Nash will be sidelined Thursday night against the Anaheim Ducks and Saturday against the St. Louis Blues, where the Rangers finish up their West Coast trip. He was sent back to New York, according to the team.
Nash sustained the injury during the first period of Tuesday's rout when Sharks defenseman Brad Stuart delivered an illegal check to the head. He did not return to the game and told reporters afterward he had a "headache."
Stuart earned a three-game suspension for the hit, the NHL's Department of Player Safety announced Wednesday.
Nash has a concussion history and missed time last season after a crushing blow from Boston's Milan Lucic sidelined him in February.
The Rangers have won only once in their first three games under new coach Alain Vigneault, and they are now missing two of their top six forwards. The Rangers are also without speedy winger Carl Hagelin, who is on long-term injury reserve as he recovers from offseason shoulder surgery.