The 23-year-old, who made his England debut in Monday’s 3-0 win in Lithuania in the final Euro 2016 qualifier, sustained the injury in training at Melwood on Wednesday.
It is the second major injury setback for new manager Jurgen Klopp after 18-year-old defender Joe Gomez was ruled out for the season after damaging an anterior cruciate ligament in England U21s’ 3-0 win against Kazakhstan on Tuesday night.
Ings’ hopes of being involved in Roy Hodgson’s squad for next summer’s tournament in France are now in serious jeopardy.
He will definitely miss the friendlies with Spain and France next month and is unlikely to be available for the clash with Germany next March.
Meanwhile, Klopp has reassured Gomez he is happy to wait for him to return to fitness.
He said: “The information about young Joe Gomez is not the best. He came back here and I met him for the first time.
“What a wonderful young boy: Tall, muscles in the right positions, but he has an injured knee, an ACL.
“We have to make a further diagnosis and we will see when he gets operated on but from this point on he can count the days until he comes back.
“It was not the best day in his life but he is a young guy and I am pretty good at waiting for players, young players especially.
“This is his home and we will do everything to help him come back as soon as possible.”
England U21 coach Gareth Southgate expressed his disappointment at the news of Gomez’s injury.
Southgate said: “First and foremost, our thoughts and best wishes are with him.
“All of us were shocked to learn the severity of Joe’s injury, not least given the symptoms displayed during the pitch assessment and on further examinations after the game.
“We took the immediate decision to substitute him following the incident so as not to take any risk.
“I have spoken with Joe and, on behalf of all the England U21 players and staff, wished him a full and speedy recovery and we look forward to his return.”
Earlier, Klopp urged his players to be brave, rediscover the fun in football and forget about making mistakes.
The German was both positive and pragmatic in his first pre-match press conference having been appointed as Brendan Rodgers’ successor a week ago.
Klopp has been preaching that to his squad as they returned in dribs and drabs from international duty during the week, and while he has not had a great deal of time to effect many changes he expects to see the players at least approach tomorrow’s early kick-off at Tottenham with a new mindset.
“Some things you can change instantly: Mentality, readiness. That is all you can change. It is not fixed that you cannot do more,” he said.
“To get really tuned as a team takes time but I am really not interested in the problems we could have on Saturday.
“I want to see more bravery, more fun in their eyes. I want to see that they like what they do, I saw that in the week and that is good. We want to get back trust from outside, get back confidence in our own skills, our own quality.
“It is the bravery we need in football, the bravery to make faults. It doesn’t work without faults. Never in history.
“As a human being we always think about faults, we don’t think about the good things. That is what we have to learn again.
“It is not important how many faults are made in the game, it is very important that no-one can remember the faults after the game.
“That is where we can always get better, to accept that something is not the best decision in your life.
“Football works because you are prepared for your team-mate making a fault and you can help him.
“You don’t have to always try the most risky ball in our lives, you have to learn to run and fight and do everything until the moment, and when the moment is there, take it.”