The Portugal international sustained the injury during his side’s 4-2 win at Manchester United on Thursday, which left the Reds’ hopes of qualifying for the Champions League in their own hands.
Liverpool will finish in the Premier League’s top four if they win their remaining three matches to West Brom, Burnley and Crystal Palace, but they will have to do it without Jota, who has scored nine goals in his first season at the club.
“No good thing without a bad thing – so, we won at Manchester United but Diogo got something with the bone,” Klopp told Sky Sports before his side’s match with relegated West Brom.
“Not too serious but serious enough to end the season. That’s it.”
Sadio Mane returns to the side in Jota’s absence after the Senegal forward was dropped for the visit to Old Trafford on Thursday.
Liverpool are already without several players for the remainder of the campaign.
Defenders Joe Gomez and Virgil van Dijk have missed most of the season, while Joel Matip joined them early in the new year.
Captain Jordan Henderson will not play again this term either and is in a race to be fit for Euro 2020 - but Van Dijk has confirmed he will not feature for Netherlands this summer.