BBC home affairs correspondent Andy Tighe said the death would be very embarrassing for the Prison Service, coming after Soham murderer Ian Huntley attempted suicide by taking a drugs overdose in Woodhill Prison last year.
Fred West was found hanged in his cell in Birmingham on New Year's Day 1995 while awaiting trial for multiple murders.
Marjorie Wallace, chief executive of mental health charity Sane, said: "The death of Harold Shipman exposes what we already know.
"The prison psychiatric services are threadbare and unable to supervise either those with known mental illness or a history of suicide attempts."
But Brian Caton, of the Prison Officers' Association, said Shipman had given no indication of suicide in interviews or in his interaction with prison officers.
Last month it emerged that the serial killer had been stripped of his
privileges at Wakefield because of poor behaviour.
But the benefits - such as a television in his cell and the right to wear personal clothing - were returned last week.
You used a calculating and cold-blooded perversion of your medical skills
Mr Justice Thayne Forbes Shipman trial judge
A police officer read a statement to the media from outside Primrose Shipman's house in
Walshford, West Yorkshire.
It said there would be no comment from the Shipman family and added: "They have asked you to respect their privacy. This is a very upsetting time
Within hours of his death, the word
"justice" had been scrawled 12 times across his former surgery in Hyde.
The vast majority of Shipman's victims were elderly women who were given lethal heroin injections.
He was brought to justice after attempting to forge the £386,000 will
of one of his victims, Kathleen Grundy, 81.
After the trial, a public inquiry was launched into how the GP was able to escape detection for so long.
It was chaired by High Court judge Dame Janet Smith, whose first report, in 2002, found the former GP had killed at least 215 patients and possibly as many as 260.
Her final report is due out in the summer.
Of Shipman's 215 likely victims, 171 were women and 44 were men.
The oldest was a 93-year-old woman, the youngest a 41-year-old man.