The 32-year-old intruder, who was arrested Sunday night, struggled briefly with police before he was pinned and handcuffed.
The man was in custody at a central London police station on suspicion of affray, or fighting, and assaulting a police officer. Police said the man, whose name has not been released, tried to lunge at an officer, but was not wielding the knife found in his possession.
"The incident will prompt a review of security, as is routine," a police spokesman said, speaking on condition of anonymity in line with department policy.
The intruder was arrested before he could have climbed another wall into the gardens of the stately home, police said, adding that the prime minister and his family were not at risk.
Police stressed that the man was challenged immediately after he landed inside the residence's secured area.
The prime minister was at home, but Blair's office would not comment on the whereabouts of his family. Treasury chief Gordon Brown, who lives next door, was in Scotland with his family, his office said.
Security at the prime minister's residence has become more stringent in response to the threat of terrorism, though detectives said there is no terrorist link to this incident. Large metal gates and armed police officers protect the front entrance to the road, and tourists often gather in front of them to peer down the narrow street.
There was a more serious security breach in 1994 when the Irish Republican Army fired a mortar from a nearby street into the garden at No. 10. The blast shattered glass, but Prime Minister John Major and members of his Cabinet, who were meeting at the time, escaped injury.
In 2000, a disturbed man crashed his car into the iron gates at the main entrance to the street, injuring an American tourist.
In 1982, a man scaled the walls around nearby Buckingham Palace and spent more than 10 minutes talking to Queen Elizabeth II in her bedroom.