"We have arrested a man in Parliament Square on suspicion of causing criminal damage to the Winston Churchill statue".
Yellow graffiti was daubed on its plinth, including the words "is a racist".
London mayor Sadiq Khan said: "This appalling vandalism is completely unacceptable".
The Metropolitan Police confirmed protesters had dispersed after 7pm, in line with conditions imposed on the event.
Extinction Rebellion's latest stunts included several naked activists gluing themselves to the shop window of fashion chain H&M's Oxford Street store, while others attempted to blockade Parliament.
The environmental demonstrations ended on Thursday with topless women protesting outside the Palace of Westminster.
They were part of a larger group from the XR campaign, which have used attention-grabbing techniques to highlight their concerns about the threats facing the planet.
The women called on the government to inform the public about the risks of allowing average global temperatures to rise by 4 degrees centigrade, which Extinction Rebellion says is what will happen by 2100 unless countries take action now. "That is why we took swift action to make a number of arrests", she said.
Commander Jane Connors described the protests as a "significant challenge" during the current public health crisis.
Prime Minister Boris Johnson said at the time it was "absurd and deplorable" that Churchill's statue should have been in danger and he would resist any attempt to have it removed.