The forward was forced off in the first half of Thursday night’s 2-2 Nations League draw in Amsterdam after taking a challenge from Quinten Timber.
Germany head coach Jürgen Klopp said after the match that Havertz was unlikely to feature again during the current international break.
“Probably out for us, but hopefully then also relatively quickly available again,” Klopp said.
The German Football Association has described Havertz’s problem as a muscle strain, with the 27-year-old now leaving the national team camp to return to his club.
Further tests will determine the extent of the injury, with Arsenal hopeful that Havertz has avoided a significant lay-off.
The timing gives the forward some recovery time, with Arsenal not playing again until they host Leeds at the Emirates Stadium on October 10.
Havertz had made a strong start to the season after overcoming injury problems that restricted him last term. He scored in Arsenal’s Community Shield victory over Manchester City and had started all five of their Premier League matches.
He has also already matched his league goal tally from the whole of last season, scoring twice in the opening weeks of the campaign.
Arsenal will now await the results of the additional examinations before determining how long Havertz could be unavailable.
The forward’s previous hamstring problems included an injury suffered during a mid-season training camp in Dubai that kept him out for a significant part of the 2024/25 campaign.