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Greene suffered a back injury during the Kings' 5-2 loss to the Chicago Blackhawks in their season opener.
In an e-mail to Lisa Dillman of the L.A. Times, Kings general manager Dean Lombardi said Greene is "out for the year probably."
To take his roster spot, the Kings have recalled defenseman Andrew Bodnarchuk from the Manchester Monarchs of the American Hockey League. Bodnarchuk played 39 games for Manchester this season, scoring three goals and nine assists. He has not played in the NHL since the 2009-10 season.
Greene had one assist on Saturday, in what would be his one and only game of the season. He played every game in the regular season during the Kings' 2011-12 championship run, tallying four goals and 11 assists.