A spokesman told AFP that the man was picked up in Berlin yesterday after flying in from Istanbul and was believed to have spent time in Syria where he allegedly joined the jihadist Islamic State of Iraq and the Levant.
He confirmed a report in the daily Frankfurter Allgemeine Zeitung, which said the man, who was not named, was hurt while fighting in Syria and posted several pictures of himself with gunshot wounds on Islamic extremist websites.
The report added that German authorities believe the man was returning to Europe to recruit other fighters for Syria or plan an attack.
"We need to exchange some information with international partners first," he said.
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The arrest came three weeks after a deadly attack on the Jewish Museum in Brussels, which police suspect was carried out by a Franco-Algerian who spent more than a year fighting for jihadists in Syria.
The French government unveiled an anti-terrorism plan in April to prevent the radicalisation of nationals, thwart online recruitment and make it more difficult for aspiring jihadists to leave the country for Syria.
The German domestic security watchdog warned recently of the threat posed by Islamic extremists returning from fighting in the Syrian civil war.