The versatile back-line option picked up a problem in the Reds' Champions League win against FC Midtjylland earlier this week, with the Selecao now confirming that the 27-year-old has suffered a right thigh muscle injury.
Liverpool have yet to confirm the severity of Fabinho's injury, but the news that he will likely miss November's international break suggests a layoff that Klopp's side can hardly afford following a spate of further absentees.
Virgil van Dijk could miss the rest of the season following an ACL injury sustained in the Merseyside derby, while fellow defender Joel Matip has also recently been sidelined, though Liverpool were able to welcome back first-choice goalkeeper Alisson in midweek.
Brazil confirmed the news of Fabinho's withdrawal with the announcement of Everton midfielder Allan as his replacement, with the former Napoli man in line to reach double-digit caps for his country next month.
"Everton midfielder Allan has been called up to the Brazil squad for the two upcoming qualifiers for the 2022 World Cup," the Selecao announced in a press statement. "The player replaces Liverpool's Fabinho, who has withdrawn with a right thigh muscle injury.
"Rodrigo Lasmar, the Brazil national team doctor, received reports and the required information from the Liverpool medical department that confirmed Fabinho would be unable to participate in Brazil's upcoming fixtures."
Fabinho's absence for Brazil, who play games against Venezuela on November 13 and Uruguay on November 17, means he is also likely out of contention for Liverpool's upcoming games against West Ham and Manchester City, and the Champions League clash with Atalanta before the international break.
Teenager Rhys Williams, who spent last term on loan at non-league Kidderminster Harriers, replaced him against Midtjylland after he was forced to come off and could be in line for his first Premier League appearance against David Moyes' side as Klopp mulls his options.
Sepp van den Berg, Nathaniel Phillips and Billy Koumetio also remain potential candidates to fill the centre-back void alongside England man Joe Gomez.