The Brazilian has been starting at centre-back in place of Virgil van Dijk, who is set to miss several months after suffering an ACL injury.
Fabinho started Tuesday's clash with Midtjylland in defence alongside Joe Gomez, but was forced out after just under half an hour.
The former Monaco man pulled up while tracking back, going to ground shortly after as he was inspected by physios.
In the minutes following, youngster Rhys Williams was summoned off the bench, with Fabinho limping off as Liverpool's centre-back concerns worsened.
Fabinho has been ever-present for the Reds since making the move from Monaco in 2018, making 41 and 39 appearances in each of his first two seasons.
The Brazilian was needed in the role due to injuries to both Van Dijk and Joel Matip, although the latter is expected to be back in the near future.
Van Dijk, meanwhile, is not, as the Dutch star suffered an injury against Everton that could keep him out for the rest of the season, although there is hope that he does return before the end of the campaign.
Williams, meanwhile, came on for his fourth senior appearance, having spent last season on loan with Kidderminster.
The 19-year-old defender featured twice for the Reds in the Carabao Cup before coming on late in Liverpool's 1-0 win over Ajax to open the Champions League group stage.
Internationally, Williams has played for England up to the Under-21 level, while he was also a member of the Liverpool squad that won the FA Youth Cup in 2018–19.
Following Tuesday's clash with Midtjylland, Liverpool will then face West Ham this weekend before visiting Atalanta on Tuesday in their third Champions League match of the campaign.