The man named as Abdalfatah HA is suspected of being part of a unit with an al-Qaeda-linked group formerly known as al-Nusra Front, which killed 36 Syrian government employees in 2013.
The federal prosecutors' office said the man, arrested in Duesseldorf, had carried out death sentences.
A second suspected al-Nusra fighter was arrested in the town of Giessen.
Abdulrahman AA is accused of breaking international weapons laws.
Both are thought to have been part of the same combat unit for al-Nusra, which was al-Qaeda's affiliate in Syria at the time.
The group formally severed its ties to the global jihadist network last year, renaming itself Jabhat Fateh al-Sham.
In January, JFS merged with four smaller groups to form Hayat Tahrir al-Sham.
German prosecutors allege Abdulrahman AA, 26, and Abdalfatah HA, 35, took part in an armed battle against Syrian government troops including taking over a big arms depot near Mahin, central Syria, in November 2013, eight months after the murders of the government employees.
Some local reports have claimed one of the men was an asylum seeker, but a spokeswoman for the prosecutors' office refused to confirm this.

Team Brewster beat the Olympic silver medallists skipped by David Murdoch 7-2 9-5 at Perth's Dewars Centre on Sunday to clinch the men's spot.
Playing third for Brewster is Glen Muirhead, brother of winning skip Eve.
Her rink claimed the women's place with three wins in a best-of-five tournament decider against Hannah Fleming's team.
"I thought it would go to three finals," said Brewster, who will be competing in his first European Championships at the event from 19-26 November.
"Dave's team were throwing the stones really well but we got off to a great start and a three in the third end gave us the lead and we managed to keep it.
"It hasn't really sunk in yet and it will be great to compete in a home event. We have trained really hard, the ice has been good this week and the guys have played great. Now we need to do more of the same at Braehead."
For Eve Muirhead, there is the excitement of playing in a European Championships in her home country.
"I think that makes a massive difference," she said.
"To get the chance to represent your country in your country is something quite special.
"Any team that's there has earned the right to be there so it will be tough as usual and I guess you've got to go there on form. Our new coach Glenn Howard's going to be there with us and he's brought a lot to this team so far."
Meanwhile, Glen Muirhead's long-term girlfriend Anna Sloan, who plays third for Team Muirhead, makes her return from injury this week.
Glen said: "It's going to be exciting for us both. We're going to be motivated to push each other on and likewise with my sister.
"It's just that extra little couple of per cent and, home soil at Braehead, so there's even more to look forward to. I'm excited and it should be fun."

It was discovered in a bin at Vere Foster Walk on Wednesday.
It is understood that the item is not linked to the police investigation into a shooting at a petrol station on the Crumlin Road in north Belfast on Sunday in which a police officer was wounded.
The suspected firearm has been taken away for examination.
A Syrian national has been arrested in Germany accused of war crimes involving the murder of dozens of civil servants.
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Scotland will be represented at next month's European Curling Championships in Braehead by rinks led by Tom Brewster and Eve Muirhead.
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A suspected firearm has been found by police during a search in west Belfast.