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."
Turkey's private NTV television quoting an unnamed passenger on board the plane said the man was demanding freedom for prisoners in Ukraine as well as former Prime Minister Yulia Tymoshenko, who is Yanukovych's top foe and serving a seven-year sentence on charges of abuse of office.
Huge protests began in Ukraine when Yanukovych shelved an agreement to deepen ties with the 28-nation European Union in favor of getting a $15 billion loan from Russia. Many Ukrainians resent the long shadow Russia has cast over Ukraine.
The protests quickly expanded their grievances to calls for Yanukovych's resignation and the denunciation of police violence after the brutal dispersal of some early peaceful rallies. The demonstrations erupted into clashes last month after Yanukovych approved harsh laws against protesters. At least three protesters died in the clashes.
Jim Heintz in Kiev contributed to this report.