The man was arrested late on Saturday in the same area as two other men and in the same neighbourhood where a Brazilian electrician, mistakenly killed by police, had lived.
The man was arrested "on suspicion of the commission, investigation or preparation of acts of terrorism," said a police spokeswoman on Sunday on condition of anonymity.
He was taken to a central London police station for further questioning, the spokeswoman said.
Two men were arrested on Friday in the south London area of Stockwell, one underground stop away from the Oval Tube station, which was one of those targeted in the 21 July bombing attempts.
Menezes was mistakenly killed by
the police (undated pic)
The latest arrest was made in nearby Tulse Hill, where Brazilian Jean Charles de Menezes had shared a flat with cousins, the police spokeswoman said.
Police also said they raided a home in Tulse Hill on Saturday, but it was not immediately clear whether that was when the third suspect was arrested.
The police declined to comment further.
Police concede mistake
In Stockwell on Friday, police shot and killed 27-year-old Menezes, mistaking him for a terrorist. The authorities acknowledged the mistake on Saturday and expressed "deep regrets".
British police described the shooting as a tragedy, while the Brazilian government demanded a full investigation.
Brazilian newspapers on Sunday reported that the victim, an electrician, might have run from plainclothes police because he was afraid they were hoodlums, or simply because he was late for work.
Menezes (2nd R) had lived in
the UK for three years
Newspapers quoted Gesio de Avila, a co-worker, as saying Menezes had called him when he entered the station to tell him he would be a little late for work. The two were to install a fire alarm in a building in northwest London.
"If he ran, it was simply because he was late," Avila told O Estado de Sao Paulo from London.
Menezes' family earlier said he was on his way to work when he was killed.
Fausto Soares, who lives in London and was a friend of the victim, told O Globo newspaper that Menezes probably ran away from the plainclothes officers because he thought they were attackers.
"He was assaulted by Englishmen (two weeks earlier) and because of that he may have been scared," said Soares, who is Brazilian.
A relative said Menezes spoke English very well and would have understood police instructions.
"My cousin was assassinated in cold blood, in an irresponsible
act against an innocent person," Menezes' cousin Alex Alves Pereira told the daily O Estado de Sao Paulo.
Pereira, who lived with Menezes in London, reportedly identified his cousin's body in a London mortuary.
"He was a worker and had nothing to do with terrorism," Pereira said, adding that his cousin did not have a past that
would make him run from police.
Menezes, who came from the city of Gonzaga in Brazil's
southeastern state of Minais Gerais, had been living legally in
Britain for three years, according to his family.
Residents and relatives in Menezes' hometown described him as a hard worker and a caring person.
"His mother is depressed, distraught, she is unable to talk. The father is also in shock"
Maria do Carmo Pereira,
The Menezes' neighbour
"His mother is depressed, distraught, she is unable to talk,"
Maria do Carmo Pereira, a neighbour of the parents, told Folha de Sao Paulo. "The father is also in shock."
Menezes' parents, Matuzinho Otoni Oliveira and Maria Otoni
Menezes, live modestly in a rural area near downtown Gonzaga.
"We still don't know what to do," another cousin, Alexandra
Alves Pereira, told Folha de Sao Paulo, adding that she felt "so
much hate, so much sadness".