The Babyshambles star, 31, was one of four people questioned following the death of the 27-year-old filmmaker.
The body of Miss Whitehead, granddaughter of the late Teddy Goldsmith – founder of The Ecologist magazine – was discovered at a flat in Hackney, east London, on January 24 after paramedics answered a 999 call.
She died from a suspected drug overdose.
Doherty was arrested in connection with the inquiry on Friday.
A spokesman for the Metropolitan Police said: "A 31-year-old man was arrested on March 19 on suspicion of supplying controlled drugs. He was bailed to return on a date in April pending further inquiries."
Doherty's friend, Peter Wolfe, 41, who found Robin's body but denied she had taken drugs, has also been arrested on suspicion of supplying controlled drugs and perverting the course of justice.
The flat's owner Gill Samworth, 53, has been arrested on suspicion of perverting the course of justice and allowing the flat to be used for the supply of drugs.
Musician Alan Wass, 28, was also arrested last Tuesday on suspicion of supplying drugs.
All three have been bailed until April.
Doherty, a friend of Miss Whitehead, said he was "shocked and saddened" following her death.
She had completed a documentary film, The Road To Albion, about Doherty's former band, The Libertines, and spent a lot of time with the singer.
Her website shows pictures of Doherty with his body encased in plaster, lying on a board in a crucifixion pose.
Her mother, Dido Whitehead, is a cousin of Jemima Khan and Zac Goldsmith, and her father is the 1960s filmmaker Peter Whitehead.