Ings suffered the injury in Southampton’s 4-3 victory over Aston Villa last Sunday.
The news will be a huge blow for Southampton who have relied upon the former Burnley and Liverpool striker as their main source of goals in recent seasons.
Ings scored 22 Premier League goals last season, missing out on the golden boot by one goal to Leicester City’s Jamie Vardy.
He has begun the current campaign with five goals and two assists in seven appearances for the Saints.
"At the moment it looks like he is out for four to six weeks," said Hasenhuttl, ahead of Friday's match against Newcastle.
"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."
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."
Aside Friday’s meeting against the Magpies, Ings will also be unavailable for matches against Wolverhampton Wanderers, Manchester United, Brighton and Hove Albion, Sheffield United and Arsenal per the time frame.
England manager Gareth Southgate will also not be able to count on Ings for November’s international games. The Three Lions are due to face the Republic of Ireland, Belgium and Iceland starting from next week.
