Ings, 23, suffered a cruciate ligament injury in his first training session with new manager Jurgen Klopp, after making his England debut in Monday's Euro 2016 qualifier against Lithuania.
Ings has scored three goals for the Reds in seven games, since joining from Burnley this summer.
Liverpool full-back Joe Gomez is out for the season with the same injury.
The 18-year-old defender was hurt while playing for England Under-21s in their 3-0 win over Kazakhstan on Tuesday.
Ings scored Liverpool's goal in their most recent Premier League game, a 1-1 draw with Everton on 4 October.
He netted 43 times in 130 games for Burnley after joining from Bournemouth in 2011.
His Clarets debut was delayed for six months after he suffered a serious knee injury in August 2011, while a knee cartilage problem led to a two-month absence the following season.
Ings joined the Reds after his Burnley contract expired but because he was under 24, the Championship club are entitled to a compensation fee, which will be decided at a tribunal.
Liverpool, who travel to Tottenham in the Premier League on Saturday (12:45 BST), are already without striker Christian Benteke because of a hamstring injury.
The Reds are 10th in the table with only one win in their past six league games.
Liverpool striker Danny Ings has been ruled out for the rest of the season with a serious knee injury.