At the opening ceremony on Thursday, President Vladimir Putin spoke of showing the world a hospitable Russia and stressed sport's ability to build bridges and overcome differences.
Tatchell's protest, held three hours before the ceremony, involved the activist unfurling a small banner near the Kremlin's walls calling attention to what his foundation described as Russia's mistreatment of LGBT+ people.
"President Putin has failed to condemn and act against the homophobic witch-hunts in Chechnya, which have seen scores of LGBT+ people arrested and tortured, with some even being killed," Tatchell said in a statement. He said he had been detained in Russia twice before.
Two men from Chechnya, a deeply conservative Muslim region of Russia, told Reuters last year they had been detained by police and subjected to torture because they were gay.
A Russian newspaper said several detainees had been killed. Chechen authorities said all such allegations were false.
Russian police quickly shut the protest down, with one officer telling Tatchell to stop what he was doing.
"During the World Cup it is forbidden to hold any action like this against Putin, against all these things," the policeman said. Tatchell told the policeman he wanted to meet Putin to discuss gay rights in Russia.
The activist said he spent an hour and 40 minutes in police custody before being released.
"Senior officers were stern but the apprehending officer very helpful, friendly and polite," the campaigner said, adding he was receiving support from the British embassy.
Britain's Foreign Secretary Boris Johnson later wrote on Twitter: "Pleased to hear @PeterTatchell is well, and my thanks to our consular staff in Moscow at @ukinrussia for providing speedy support to him."
Tatchell said he was required to appear in court on June 26, accused of breaking a federal law on the holding of public meetings and demonstrations, as well as a presidential decree that prohibits protests during the World Cup.
Piara Powar, executive director of European anti-discrimination network FARE, opened a temporary diversity centre in Moscow on Thursday to support soccer fans worried about any racism or homophobia.
Tunde Aderibigbe, head of protocol for Nigeria's football federation, said he believed the Russian government had done its best to deal with the issue of racism.
"We have been meeting a lot of (fans) and they are very cheerful. There hasn't been any cause to think there is going to be something like that," he said.
(Additional reporting by Elizabeth Piper; Writing by Andrew Osborn; Editing by Alison Williams and Andrew Heavens)
