EU border agency Frontex confirmed to AFP the arrival of the migrants with the Greek Ministry for Civil Protection saying many were bruised and naked, in an "inhuman image".
"The Frontex officers reported that the migrants were found almost naked and some of them with visible injuries," said Paulina Bakula, spokeswoman for the organisation.
The UN refugee agency, UNHCR, tweeted that it was "deeply distressed by the shocking reports and images of 92 people, who were reported to have been found at the Greek-Turkish land border, stripped of their clothes".
Ms Bakula, speaking from Frontex's headquarters in Warsaw, Poland, said Frontex officers worked with Greek authorities to provide the mainly Afghan and Syrian migrants with immediate assistance.
She said the organisation had informed the agency's fundamental rights officer of possible rights breaches.
The Greek Minister for Civil Protection, Takis Theodorikakos, accused Turkey of "instrumentalising illegal immigration" in the latest of a series of recriminations on migration between the neighbours.
Mr Theodorikakos said to Skai TV that many of the migrants told Frontex "three Turkish army vehicles had transferred them" to the river, which is a natural border.
Migrants in Greece and Turkey - in pictures
In scathing comments on Twitter, the Turkish presidency denied any responsibility for the migrants and blamed Greece for the "inhuman" situation.
"We urge Greece to abandon its harsh treatment of refugees as soon as possible, to cease its baseless and false charges against Turkey," wrote President Recep Tayyip Erdogan's top press aide, Fahrettin Altun.
"With these futile and ridiculous efforts, Greece has shown once again to the entire world that it does not respect the dignity of refugees by posting these oppressed people's pictures …"
Mr Altun accused Athens of deporting the 92 people "after extorting their personal possessions".
Turkey's deputy interior minister Ismail Catakli called on Greece to stop what in a tweet he called its "manipulations and dishonesty".
The Greek Minister for Migration and Asylum, Notis Mitarachi, on Saturday described the incident as a "shame on civilisation".
Athens regularly faces and denies accusations that it has sought to push migrants back to Turkey illegally, sometimes using force.
Last month, Mr Erdogan used a UN address to accuse Greece of turning the Aegean Sea into a "cemetery" with "oppressive policies" on immigration.
Dramatic clifftop rescue after migrants’ boat sinks in Greek waters - video
"In the Evros region, systematic human rights crimes against people on the move are committed on a daily basis by Turkey as well as Greece," German rights group Mare Liberum tweeted.
"When these crimes are publicly discussed by members of the government, it only serves to add fuel to the fire of the long conflict between Turkey and Greece, not to protect people on the move."