Doctors repaired the radial artery and two superficial radial nerves at Keck Medical Center, the team said. He will be evaluated weekly, but the team doesn't know when he will return.
"First of all, we're real happy that things went well for Alec," coach Todd McLellan said. "Now he's got some time to heal, and when he's ready to play again, we'll welcome him back because he's an important part of our team."
Martinez was hurt in the third period of the Kings' 4-3 overtime loss to the San Jose Sharks on Monday night. Martinez made a headfirst dive to bat away a loose puck and was cut just above the glove by the skate of Melker Karlsson when the Sharks forward lost his balance.
"You obviously saw him skate off the ice holding his hand, but I had no idea it was as bad as it was," defenseman Joakim Ryan said Tuesday.
The 32-year-old Martinez has five assists in 24 games this season, his 11th in the league. He became a fan favorite after scoring in overtime of Game 7 of the 2014 Western Conference finals against the Chicago Blackhawks and in Game 5 of the 2014 Stanley Cup Final against the New York Rangers to win the Kings' second title in three seasons.
Martinez was averaging 21 minutes per game, second on the team behind Drew Doughty. McLellan said Martinez's absence would give younger players a chance to be used in different roles, including on the power play and penalty kill.
"He's been around here for a while, won two Stanley Cups, so he's been through it all," Ryan said. "But injuries always create opportunities for other guys, and hopefully some guys can step up and take on a bigger role."
Derek Forbort, a four-year veteran, is nearing a return from the back injury that has kept him from playing this season. Forbort has been working out with the team and could soon begin an AHL rehab assignment.