The 18-year-old Irish international was a half-time substitute for the relegation-threatened side in a 2-0 defeat to Arsenal at the Emirates last weekend but came off after 20 minutes.
Obafemi, who last year became the first player born after the year 2000 to feature for the club in a Premier League match, had only just returned from injury.
"It's a big blow for Michael; until the end of the season he won't play," Hasenhuttl said ahead of Wednesday's home game against fellow strugglers Fulham.
The Austrian had called the situation a "disaster" immediately after the match.
Hasenhuttl said forward Danny Ings and midfielder Mario Lemina would not feature against Fulham.
"It doesn't seem like it's possible to play Danny, the risk is too high," he said of a player who has yet to return to training with the team.
"Mario Lemina is not training with the squad but he's working every day to return."
Southampton are 18th in the league, a point behind Cardiff City, while Fulham are 19th and seven points adrift of the Saints.
(Reporting by Alan Baldwin; Editing by Hugh Lawson)
