The 29-year-old defender, from Sao Paulo in Brazil, was apprehended by officers who noticed a car being driven erratically by a driver who failed to stop.
The incident happened last Friday morning - the day before the north London team's first game of the season - Scotland Yard said.
It is thought Santos, who was on the bench for the Gunners' opener against Sunderland on Saturday, was behind the wheel of a powerful sports car.
He was picked up by officers close to Arsenal's training ground in London Colney in Hertfordshire, just inside the M25 motorway.
The Sun newspaper reported a car was being driven at speeds of up to 130mph in a high-speed chase.
A Metropolitan Police spokesman said: "Shortly after 9.30am on Friday August 17, a 29-year-old man was arrested on suspicion of dangerous driving and failing to stop for police on the A1, near to Junction 22 of the M25.
"Officers' attention was drawn to the vehicle due to the manner of its driving.
"The man has been bailed to return at a date in mid-September to a north London police station."
Santos was not breathalysed, police added.