Mr Tatchell was detained for what Russian police described as an illegal protest.
He had attempted to hold a solitary protest near the Red Square to draw attention to potential human rights abuses committed against gay men in Chechnya.
A reporter for the Reuters news agency saw a Russian policeman inform Mr Tatchell that it was illegal to hold such protests during the tournament.
The policeman told Mr Tatchell that he had to stop or he would be detained.
After what was described as a “long conversation”, Tatchell was led away to a waiting police car.