The 28-year-old's absence will be a major blow for the Bulgarian champions who were drawn in Group B, also containing winners Real Madrid and Swiss champions Basel.
"Cvorovic won't be able to play against Liverpool, he sustained the injury during yesterday's training," Ludogorets coach Georgi Dermendzhiev told reporters after their 2-1 win at Botev Plovdiv on Friday.
"It's a serious injury and he'll probably undergo surgery on Monday."
Ludogorets, who are based in Razgrad – a town with a population of less than 35,000, will also be without their first choice keeper Vladislav Stoyanov, who is suspended after being sent off in their dramatic shootout win over Steaua Bucharest in the second leg of the playoff round.
Romania defender Cosmin Moti was forced into goal for the penalties and made two saves to send the Bulgarians into the group stage for the first time.
Ludogorets then decided to name a new stand at their Ludogorets Arena after Moti.
Stoyanov and Cvorovic are Bulgarian internationals and were the two keepers in the Balkan country's squad for their 2-1 win in Azerbaijan in a Euro 2016 qualifier on Tuesday.
Dermendzhiev will now have to turn to Georgi Argilashki, who has been part of a Ludogorets squad which has won three successive league titles since 2012 but is yet to make his league debut.
"Argilashki is a quality keeper," said Dermendzhiev. "He was part of the team for three years now and we can rely on him."
The Eagles became only the second Bulgarian club to reach the group stages after Levski Sofia in 2006.
(Reporting by Angel Krasimirov)
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