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.
Liverpool defender Virgil van Dijk believes the Netherlands can make significant progress under new head coach Xavi Hernandez after beginning his tenure with a 1-1 draw against Germany.
Leeds United star Ethan Ampadu has demanded greater standards from Wales after their winless run was extended by a 1-0 Nations League loss to Portugal in Lisbon.
Rio Ngumoha believes his rapid rise into the Liverpool first team came from having the confidence to believe it could happen.
A brace from Erling Haaland led Norway to a hard-fought victory over Denmark in their UEFA Nations League opener, while Portugal edged out Wales to begin their League A campaign with a win.
