The news come a day after Zetterberg skipped a training session with the national team.
"We have reached the conclusion that the tournament is over," said team medic Björn Waldebäck.
The Detroit Red Wing star's back problems are so serious that he is not even in good enough shape to travel back home at this point.
Zetterberg suffered from back troubles earlier in the season, too, and had to pass a few matches with his NHL team. After Sweden's Olympic opening game against the Czech Republic, Zetterberg's back problems returned and on Thursday he skipped a training session.
The Swedish team is not allowed to call in an extra player at this point, meaning that they are down from 25 to 24 men. Niklas Kronwall is the new team captain, with Daniel Alfredsson the assistant captain.