Before the latest report, Kings coach Terry Murray said Kopitar would need a minimum of six weeks to recover, but Kopitar is now listed as being out indefinitely.
The surgery will be performed Wednesday.
"There's quite a hole that's going to be there now, with him out of the lineup for this length of time," Murray said. "But I've been through these kinds of things before, with top guys being out because of injuries. It's an opportunity. Other guys step up. The character of the team needs to step up."
Kopitar isn't likely to resume skating until the middle of the summer, the Kings said.
The center was trying to jar the puck loose along the left-wing boards Saturday afternoon against Colorado when he appeared to lose his balance and fall awkwardly under the weight of his right leg. Kopitar was playing in his club-record 330th consecutive game.
The Kings are also without second-leading scorer Justin Williams, who dislocated his right shoulder last week against Calgary and is out three to four weeks.
Los Angeles is in a fifth-place tie with Nashville in the Western Conference standings. The teams have 92 points apiece, but the Kings have two more victories and a game in hand, putting them in good position to earn their second straight playoff berth after an eight-year postseason absence. The Kings resume play Tuesday in Edmonton.
Dan Arritt covers the Kings for ESPNLosAngeles.com. Information from The Associated Press was used in this report.