Murray suffered the injury early in Saturday's win over the Chicago Bulls. He has been dealing with hamstring tightness since training camp.
"His injury is not one- or two-game injury," coach Michael Malone said. "That's what I do know. This is something that will be longer than we would like."
Reggie Jackson has been starting in place of Murray, but Malone said replacing Murray's minutes and production will be "by committee."
Murray is averaging 16.3 points and 7.4 assists this season for the Nuggets, who enter Monday night 6-1 atop the Western Conference.
The Associated Press contributed to this story.