The renowned physicist and lifelong Labour supporter claims the NHS is at risk of privatisation under the Tories.
The world-renowned physicist and lifelong Labour supporter claimed the NHS was at risk of privatisation under the Tories.
He said: "We see the balance of power in the UK is with private healthcare companies, and the direction of change is towards a US-style insurance system."
But Health Secretary Mr Hunt challenged the scientist to "look at the evidence".
He wrote on Twitter: "Most pernicious falsehood from Stephen Hawking is idea govt wants US-style insurance system. Is it 2 much to ask him to look at evidence?
"NHS under Cons has seen more money, more docs and more nurses than ever in history. Those with private med insurance DOWN 9.4% since 2009!"
Professor Hawking also accused the Heath Secretary of "cherry-picking" favourable evidence to justify NHS reforms to create a seven-day service.
Under his drive for a seven-day service, Mr Hunt moved to reform junior doctor contracts, which led to a number of strikes by medics.
Mr Hunt wrote on Twitter: "Stephen Hawking is brilliant physicist but wrong on lack of evidence for weekend effect.
"2015 Fremantle study most comprehensive ever... and whatever entrenched opposition, no responsible Health Sec could ignore it if you want NHS 2 be safest health service in world as I do."
The Fremantle Study looked at data from 2013 and 2014 and found that, although there were fewer hospital admissions at weekends, patients who were admitted during that time were sicker and faced an increased likelihood of death within 30 days, even when the severity of illness was taken into account.
Prof Hawking, who is director of research at the Centre for Theoretical Cosmology at the University of Cambridge, warned Mr Hunt's actions were harmful at a time when public support for science is "more important than ever".
He wrote: "Hunt had cherry-picked research to justify his argument. For a scientist, cherry-picking evidence is unacceptable.
"When public figures abuse scientific argument, citing some studies but suppressing others to justify policies they want to implement for other reasons, it debases scientific culture."
The 75-year-old, who was diagnosed with motor neurone disease in 1962, also said he "would not be here today if it were not for the service".
Labour leader Jeremy Corbyn called the physicist a "brilliant scientist" with a "brilliant mind" and "brilliant thought process".
He added: "If Stephen Hawking is saying that our NHS is under threat and in danger and in crisis then I think we need to listen very very carefully with what he has to say."
And former Liberal Democrat boss Tim Farron said: "A renowned scientist such as Stephen Hawking questioning your evidence might normally be cause to think again, but sadly it looks as though Jeremy Hunt has joined the chorus of those who have had enough of experts."