The foiled hijacking took place as thousands of athletes from around the world poured into a tightly-secured stadium in Sochi amid warnings the games could be a terror target.
The man was being questioned by police for possible links to terror groups, according to Turkey's state-run TRT television. It wasn't clear when charges would be brought.
"We think it was an individual thing," Transport Minister Lutfi Elvan told reporters in response to questions on to whether the incident was a "terrorist" act. "It may be linked to (events in) Ukraine... Our colleagues say it is not a serious issue."
Maxim Lenko, the head of the Ukrainian Security Service's investigative division, said the Kharkiv resident wanted to divert the plane to Sochi where Russian President Vladimir Putin and Ukrainian President Viktor Yanukovych were meeting on the sidelines of the Olympics.
"The passenger put forth the demand to free the 'hostages' in Ukraine," Lenko said, in reference to people arrested in the ongoing protests in Ukraine. "Otherwise, he threatened to blow up the plane."