Doherty, 31, has battled an addiction to drugs for years and has spent time in jail and rehab because of it.
The 27-year-old Whitehead, a filmmaker, was the granddaughter of Teddy Goldsmith, the founder of The Ecologist magazine. She was the great-niece of billionaire James Goldsmith.
Whitehead was found dead in a London apartment in January.
The Times of London said Doherty was arrested Friday in connection with the death of his friend. He has since been released on bail.
Doherty is expected to return to court next month for another hearing on the matter, the newspaper said.
Whitehead and Doherty had collaborated on a documentary about Doherty's former band The Libertines shortly before her death.