Pogba limped off in the opening ten minutes in Manchester United's 4-0 loss to Liverpool in the Premier League on Tuesday.
It has been revealed that it was a calf injury that forced Pogba off as Manchester United dropped to sixth on the table.
The 29-year-old is out of contract at the end of the season and it is unlikely that he will extend his stay at Old Trafford.
2021/2022 has largely been a campaign disrupted by injury for Pogba, who has made 27 appearances across all competitions, scoring one goal and providing nine assists.
The France international, who is in his second spell with the Red Devils, has been linked with former club Juventus and Paris Saint Germain.
"It is very unlikely that he will play until the end of the season again," Rangnick said.
"The doctor told me that it will take four weeks minimum for him to recover and since last game is at end of May, I don't think it's very likely he will play again."
The Red Devils will however be boosted by the return of Cristiano Ronaldo for Saturday's trip to Arsenal.
Ronaldo missed the Liverpool game following the death of his new born son.
Providing an update on the eve of the Arsenal match, Rangnick said: "Cristiano has been training with us and is available again."
Manchester United have five games left before the season ends, with their last match coming against Crystal Palace on May 22.
