Sweden made the announcement Friday before facing Switzerland in its second game of the tournament.
Zetterberg scored a goal in the Swedes' opening victory over the Czech Republic on Wednesday. He sat out of Thursday's practice because of a herniated disk in his back.
The injury also has bothered the Swedes' first-line centre during the NHL season with the Detroit Red Wings, forcing him to miss 11 games.
Zetterberg is a four-time Olympian who won a gold medal with Sweden in Turin in 2006. His absence is another blow to the Swedes, who were a medal favourite before Henrik Sedin and Johan Franzen were forced to skip the Olympics with injuries.