Zetterberg played through pain and scored a goal in Sweden's opening victory over the Czech Republic last week at the Sochi Olympics, but that was his only appearance before he left because of a herniated disk.
Zetterberg has 16 goals and 32 assists in 45 games for the Red Wings this season. Detroit is fighting for a playoff spot in the Eastern Conference, and it now seems the Red Wings will be without the 33-year-old centre for most if not all of the stretch run.
The Red Wings say the operation was performed by Dr. Frank Cammisa in New York.
Zetterberg won an Olympic gold medal in Turin in 2006, and the Swedes have reached the gold medal game this year against Canada without him.
Zetterberg's nagging back injury kept him out of several games with the Red Wings earlier this season. If the season ended now, Detroit would hold the last post-season spot in the East, but the franchise's streak of playoff appearances has looked increasingly tenuous lately.
The Red Wings haven't missed the post-season since 1990. They finished third in their division last year but were able to beat Anaheim in the first round and then took eventual champion Chicago to seven games before being eliminated.
Zetterberg has 12 more points this season than any other Detroit player. Defenceman Niklas Kronwall is second on the team with 36 points.