The Swedes will face France in the round of 32 after advancing as one of the eight best third-placed teams, but the 27-year-old will be unavailable for coach Graham Potter.
"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," national team doctor Jonas Werner said in a statement released by the SvFF on Friday.
"He will return to his club, and the injury means that he will be away from football for some time."
Potter said they would offer Hien their full support in his recovery.
"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," he said in the statement.
"It's sad for him, but I'm sure he'll come back stronger."