The Brazil international left-back, 29, was detained near the north London club's training ground in the county of Hertfordshire, north of the British capital, last Friday morning.
Police said the vehicle involved was a powerful black Maserati sportscar which officers noticed was being driven erratically and which failed to stop.
A Metropolitan Police spokesman said: "Shortly after 9:30 am (0830 GMT) 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."
The man was not breathalysed, police added.
Santos was on the bench for the Gunners' home game against Sunderland on Saturday.
He has made 15 appearances for Arsenal since joining the club from Turkish side Fenerbahce for ?5.5 million pounds (seven million euros, $8.7 million) in August 2011.
Source: AFP
Source: AFP