As he was being taken away by police, Tatchell said: "This shows the Russian people are not free."
Among those detained was Nikolai Alexeyev, a Russian gay rights leader.
Police said they were arresting him for walking with a transvestite.
Earlier on Saturday, a counter-demonstration by nationalist and religious groups was allowed to be held.
Yuri Luzhkov, the Moscow mayor, has taken a hard stand against homosexual protesters, once describing gay parades as "satanic".
Alexeyev told Al Jazeera: "We are not just going to surrender because the Moscow mayor who is breaching the law of the constitution and the European convention is deciding this alone and taking full responsibility for what is going on."
|Alexeyev, a Russian gay rights leader, was among those detained in Moscow [AFP]
Europe's most prestigious pop music contest has drawn attention to gay rights in Russia, with some singers threatening to boycott the event if the gay pride parade was not allowed to happen.
In previous years there have been many attacks on members of the gay community during similar attempts to hold demonstrations.
Al Jazeera's Neave Barker, reporting from Moscow said: "With forty-two million dollars spent on the stage alone, this is the grandest Eurovision ever.
"The winner is even expected to be announced by the crew on board the International Space Station.
"And while dubbed the most ostentatious Eurovision yet, the event is also likely to go down in history as the most politically charged."