Ings had a scan after injuring his knee during Southampton's 4-3 Premier League victory at Aston Villa on Sunday.
"At the moment it looks like he is out for four to six weeks," said Hasenhuttl.
"He'll have a small surgery tomorrow (Thursday) morning. It could be worse, but he'll be out and it's not good news for us."
Ings went off five minutes from time after being injured in a challenge with Villa substitute Trezeguet, having scored his fifth league goal of the season earlier in the game.
Now the 28-year-old former Burnley and Liverpool forward, who has previously suffered two serious knee injuries, will now be absent as the Saints look to build on an impressive start to the season.
The south coast club are currently fifth in the table, and play Newcastle, Wolves, Manchester United, Brighton, Sheffield United and Arsenal in the next six weeks.
Hasenhuttl added: "We are more than Danny Ings. It's a big loss but it's important now for other players to give us alternatives.
"Nobody has to play like Danny Ings, every player should play his best possible game."
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