He will be placed on injured reserve and will have surgery in a few weeks after the swelling goes down.
Coach Bruce Arians made the announcement at his early-afternoon news conference one day after the Cardinals beat the San Francisco 49ers 18-15 in overtime.
"It breaks everybody's heart in there because they know how hard he plays. It takes a lot of spirit out of the defense because he brings it every play," Arians said.
Golden suffered the injury with 7:30 left in overtime during an incomplete pass by San Francisco quarterback Brian Hoyer. Golden was flagged for defensive offsides on the play.
Golden, who's in his third season, didn't have a sack through four games after finishing last year with 12.5.
Kareem Martin will likely replace Golden in the starting lineup.
Golden was part of Arizona's dangerous pass-rush tandem along with Chandler Jones. Last year, the two combined for 23.5 sacks becoming the first Cardinals' tandem to combine for double-digit sacks since 1984.
"It is really difficult to see Markus (Golden) go down like that, but Kareem (Martin) has been waiting for an opportunity, and he's going to have his now," quarterback Carson Palmer said. "We are as good of a defense as there is in this league."