Varoufakis said he had just landed at Charles de Gaulle Airport on a flight from Athens when a police officer standing near the plane ramp asked to see his passport, AFP reported.
Varoufakis said he complied, but the officer subsequently left him little room as he tried to pass.
"The moment our elbows touched, he reacted violently," the economist said.
"(He) manhandled me, using physical violence," Varoufakis told AFP, adding that the officer pushed him, grabbed his passport and told him to stand against the wall.
Two more superior officers had to be summoned before Varoufakis' passport was returned.
"I am formally requesting a formal apology from the French police," he said.
One of the officers said he also plans to lodge a complaint against Varoufakis.
A former finance minister under leftist prime minister, Alexis Tsipras in 2015, Varoufakis last week became a member of Greece's parliament, one of nine lawmakers elected by his anti-austerity MeRA25 Party in general elections.