The man was apprehended after disembarking from a cruise ship on the island of Mykonos on Thursday, a Greek police official said.
Authorities said there was a European arrest warrant issued by Germany for the hijacking.
He was also wanted in connection with a 1987 kidnapping crime, which could be related to his release in return for the freeing of two German citizens held hostage by his accomplices in Lebanon, said the policeman.
The suspect is being held in a high-security prison until German authorities identify him as the person wanted, they added.
The German federal prosecutor’s office declined to comment on the case.
The TWA 847 flight from Cairo to San Diego with several en route stops was hijacked shortly after taking off from Athens in 1985. The hijackers demanded the release of Shi’ite Muslim prisoners from Israeli custody.
Some passengers were beaten and a U.S. Navy diver who was on board the aircraft was beaten and murdered. They released the other 146 passengers and crew members on the plane in stages during an ordeal that included making three stops in Beirut and two in Algiers.
The last hostage was freed after 17 days.