The Arsenal forward lasted only 30 minutes before being replaced by Younes Ebnoutalib after appearing to suffer a hamstring injury.
Havertz went down following a heavy challenge from Dutch midfielder Quinten Timber, the brother of his Arsenal team-mate Jurrien Timber. He initially tried to continue but was eventually forced off after appearing to feel discomfort at the back of his thigh.
Klopp confirmed after the match that Havertz and Jamal Musiala, who picked up a thigh problem during the warm-up, would both undergo MRI scans.
"Both will undergo MRI scans tonight and then we'll have the diagnoses," Klopp said.
"They're probably out for us, but I hope they'll be back soon (for their clubs)."
The timing of the injury will concern Arsenal, with Havertz expected to return to club duty after the international break.
Arsenal host Leeds in the Premier League on October 10, with the club now waiting for the results of Havertz's scan to discover whether he will be available.
Norway have withdrawn Erling Haaland from Saturday's scheduled press conference ahead of Sunday's Nations League clash with Portugal in Oslo, following reports surrounding Manchester City's financial case.
Liverpool have brought Julian Ward back as sporting director, with the 45-year-old returning to the position following Richard Hughes' departure.
Rodri has backed Manchester City to prove their innocence and insisted nothing can take away the success he enjoyed at the club.
Zinedine Zidane began his France reign with a hard-fought 1-0 win over Turkey, but the new head coach warned his players that tactical balance will be crucial to their success.
