Doherty, 26, was stopped by police as he drove along a street in west London early Wednesday, said spokesman Tony Linkin.
The Metropolitan Police said officers had stopped a car that was driving erratically in the area. Police said "substances" were found and a 26-year-old man was arrested on suspicion of possessing Class A drugs — a category that includes cocaine and heroin.
The driver was taken to a local police station and later released on bail. He is due to report back next month.
His relationship with Moss coincided with her own well-publicized drug problems. She checked into an Arizona rehab clinic in September after a tabloid newspaper published pictures that allegedly showed her taking cocaine.