The 24-year-old was stopped by police while driving his Audi Q7 on Victoria Embankment near the River Thames.
Cole was given a roadside breath test and taken to a nearby police station where he was later bailed.
A Metropolitan Police spokeswoman said: "At about 4.25am on September 23, police pulled over an Audi Q7 on Victoria Embankment, SW1.
"A 24-year-old driver was spoken to and subsequently arrested on suspicion of driving with excess alcohol. He was taken to a central London police station and bailed to return on a date in mid-November."
Cole was rested for the club's tie against Watford on Tuesday evening because of a foot injury.
West Ham manager, Gianfranco Zola, has said Cole has the potential to play for England if his performance on the pitch continues to improve.