The Brazilian was apprehended by officers after driving his car erratically, at reported speeds of 130mph on the M25 motorway and for failing to stop accordingly for them.
The alleged incident took place last Friday morning the day before the Gunners kicked off their Premier League campaign against Sunderland, where Santos was named on the bench.
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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."