Photos show Lebedev pulling out a flag and being wrestled to the snow by men described as Olympic security personnel by the AP.
“Hosting the Games here contradicts the basic principles of the Olympics, which is to cultivate tolerance,” Lebedev said in a phone interview while at the police station, according to the AP.
In June, Russian president Vladimir Putin signed a law banning the promotion of non-traditional sexual relations toward minors.
In August, the International Olympic Committee said it received assurances from the highest level of Russian government that the legislation will not affect those attending or taking part in the Games.
Protests at the Olympics will be allowed in designated areas if approved by Russian authorities.