Regehr suffered the undisclosed injury in the first period. Since the Kings didn't offer any specifics (which is normal gamesmanship during the playoffs), we can only speculate about what exactly caused Regehr to leave the ice. But for what it's worth, he was hit rather hard by Teemu Selanne on his last shift of the game.
At any rate, the Kings will miss Regehr's presence if he's out for an extended amount of time.
Regehr was traded for from the Buffalo Sabres in 2013 and quickly signed a two-year contract with the Kings in the second round of last season's playoffs. He recorded three goals and 14 points in 79 games during the regular season, and has just two assists during this year's playoffs.