The 55-year-old citizen of the Netherlands, whose name was given as Musa A., was arrested in Hamburg, Germany's federal prosecutor said.
The man is thought to be a "leader" of the Revolutionary People'sLiberation Party /Front (DHKP-C) -- a radical Marxist group outlawed by Ankara after allegedly staging several attacks and assassinations against police, the security services and US interests in Turkey.
The prosecutor said he was carrying out several roles in Europe, principally fundraising for the European arm of the DHKP-C.
German authorities believe that such fundraising could be used to finance terrorist activity and the acquisition of weapons.
Musa A. will appear in court on Monday before a judge who will rule whether to remand him in custody.
In August 2015, the DHKP-C claimed responsibility for an attack in Istanbul by two of its militants on police guarding the offices of Prime Minister Ahmet Davutoglu. No one was hurt.
The arrest comes just weeks after Turkish President Recep Tayyip Erdogan accused Germany of "hosting terrorists".
Berlin and Ankara have been at loggerheads recently with Germany -- a vocal critic of Erdogan's widespread crackdown on opposition politicians, journalists and teachers as well as the military and police in the wake of a failed coup in July.
Chancellor Angela Merkel has described the Turkish crackdown as "highly alarming".
Turkey's increasingly authoritarian leader also accused Germany of harbouring members of both the DHKP-C and the outlawed Kurdistan Workers Party (PKK).
Both groups are branded terrorists by Turkey, the US and the EU.