"He has major problems due to a back injury and it's become so painful that he can't participate," team doctor Björn Waldebäck told the Aftonbladet newspaper.
"There's no chance that he'll be able to practice or play a game during the time we're here."
Team officials explained that Zetterberg's herniated disk is so serious that he can't even get on a plane to fly home.
While the 33-year-old Detroit Red Wings star managed to score a goal in Wednesday's 4-2 victory over the Czech Republic, the back problems that have plagued him during the NHL season flared up following the match.
The loss of Zetterberg to injury comes just hours before Sweden's match against Switzerland and leaves Tre Kronor one man short for the remainder of the tournament.
Fellow Red Wings teammate Niklas Kronwall will take over as team captain, with assistant captain duties shifting to Daniel Alfredsson.
Sweden now find themselves without two of its top players, as Vancouver Canucks forward Henrik Sedin was unable to make the trip to Sochi due to a rib injury.
Ahead of the tournament, Sweden was tapped as a favourite to pick up another Olympic ice hockey medal after missing the podium in Vancouver in 2010.