The 24-year-old striker was stopped in his Audi Q7 on Victoria Embankment near the River Thames at 4.25am.
He was given a roadside breath test and taken to a nearby police station, where he was later bailed to return in mid-November.
West Ham manager Gianfranco Zola said he was "very disappointed" Cole had been out so late but was confident the former England Under-21 international had learned his lesson.
"I spoke to him and he is very sorry at being out at such a time," said Zola.
"He wasn't drunk, which was a very good thing. He has just been out late in the night.
"He will be fined, he knows that. We are going to deal with it but the player understood 100% that he made a mistake. He is ready to take the fine the club is going to give him."
Zola has been impressed by Cole's development, both on and off the field, since he last encountered him as a team-mate at Chelsea.
Last weekend Zola suggested Cole had the potential to play for England after his performance as a lone striker in West Ham's 3-1 victory over Newcastle.
Now Zola has warned Cole any international aspirations could be scuppered by a lack of discipline.
"I am disappointed with him but that doesn't take away all the chances that he has got," said the Italian.
"He knows that he can't do this kind of thing, especially if he wants to achieve high levels. If he wants to play for the national team he can't afford to do things like that.
"He has realised and he is very sorry for that.
"Carlton is a changed player. He is very much matured. He knows he has got a great chance and I am sure he is going to take it."