Julian Assange is being held in Belmarsh ahead of a hearing on 24 February.
The 117-strong group penned an open letter in The Lancet medical journal, calling for an end to what it described as "the psychological torture and medical neglect" of the WikiLeaks founder.
Mr Assange is being held in Belmarsh prison ahead of a hearing on 24 February which could result in him being extradited to the US.
The 48-year-old faces 18 charges in the US, including conspiring to hack into a classified Pentagon computer.
The letter says: "Assange is in a dire state of health due to the effects of prolonged psychological torture in both the Ecuadorian embassy and Belmarsh prison, where he has been arbitrarily detained according to the UN Working Group on Arbitrary Detention.
"Should Assange die in a UK prison, as the UN special rapporteur on torture has warned, he will have effectively been tortured to death.
"The medical profession cannot afford to stand silently by, on the wrong side of torture and the wrong side of history, while such a travesty unfolds."
The letter also sets out accusations of "politically motivated medical neglect" which it says "sets a dangerous precedent".
Supporters of Julian Assange hold signs outside Westminster Magistrates' Court
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"Our appeals are simple: we are calling upon governments to end the torture of Mr Assange and ensure his access to the best available healthcare, before it is too late."
A copy of the letter has been sent to the UK government and the Australian minister for foreign affairs, Marise Payne.
The Doctors for Assange group has previously written to the home secretary and the Australian government to express concern for his welfare.
In a November 2019 letter, the group said it had "serious concerns" about his fitness to stand trial.
Last year, UN special rapporteur on torture Nils Melzer visited the WikiLeaks founder in Belmarsh and reported that he "showed all symptoms typical for prolonged exposure to psychological torture, including extreme stress, chronic anxiety and intense psychological trauma".
Mr Melzer later warned Assange's treatment in prison "may soon end up costing his life".
Assange has been in custody since he was removed from the Ecuadorian embassy in April 2019 after his asylum status was withdrawn.
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