He will be replaced by St. Louis goalie Brian Elliott.
The Blue Jackets did not reveal a timetable for Bobrovsky's return.
Bobrovsky, selected to participate in his first All-Star game, has a 16-15-2 record with a 2.85 goals-against average, .913 save percentage and one shutout in 33 games this season. He landed awkwardly while making a stop in the second period of the game won 4-0 by the Jets.
The 2013 Vezina Trophy winner as the NHL's top goalie, he underwent tests on Thursday afternoon.