It was after a knee-high kick from Dutchman Quinten Timber that Havertz was forced to miss Thursday night's meeting in Amsterdam.
The striker was scheduled to undergo an MRI scan later in the evening, as was his national teammate Jamal Musiala.
"I hope it's nothing serious. The guys are probably out for us. But hopefully they'll be back in the game relatively quickly," new head coach Jürgen Klopp told RTL, according to Sky Sports.
On Friday, the German federation announced that the duo was leaving the squad.
Havertz has started all five Premier League matches for Arsenal this season, while Viktor Gyökeres has been benched in three and made only short appearances in the other two.
