The 27-year-old picked up the injury during Sweden's 1-1 draw against Japan on Thursday. Sweden still progressed to the knockout stage as one of the eight best third-placed teams, but they will now have to face France without one of their key defenders.
The Swedish Football Association confirmed on Friday that Hien would take no further part in the competition after medical examinations revealed the extent of the problem.
National team doctor Jonas Werner said: "Isak has sustained an injury in his left hamstring to such an extent that he will not be able to participate further in the World Cup.
"He will return to his club, and the injury means that he will be away from football for some time."
The news is a significant blow for Sweden coach Graham Potter, who had relied on Hien's defensive qualities during the group stage. With a place in the last 16 at stake against France, Potter will now have to reshuffle his back line.
Despite the disappointment, Potter backed the defender to recover fully and return stronger.
"Having to end the World Cup in this way with an injury is very sad and we will support him in the best way possible," Potter said.
"It's sad for him, but I'm sure he'll come back stronger."
Hien will now begin his rehabilitation with his club while Sweden prepare for one of their toughest tests of the tournament.