In a speech on Saturday, the Cambridge University scientist is expected to accuse Jeremy Hunt of "cherry-picking" evidence to support his policies.
And he will also say he is concerned about the involvement of the private sector in the NHS in England.
But the government has defended its record on the health service.
A statement released by the Department of Health after the text of the speech was given to the BBC in advance, pointed out that extra money was being invested in the NHS and it had recently been ranked as a top-performing health system.
Prof Hawking, who has had motor neurone disease for most of his adult life that has impaired his movement and ability to speak, will deliver the speech at a conference at the Royal Society of Medicine in London organised to air concerns about the future of the NHS.
The author of A Brief History of Time, who is a Labour supporter, will say he has been motivated to speak because of the role the health service has played in his life, saying if it was not for the NHS he "wouldn't be here today".
In the speech, Prof Hawking will list a number of occasions on which the NHS was there for him.
They include an episode in 1985 when he caught pneumonia in Switzerland.
Doctors there suggested his ventilator be turned off to end his life, but his wife refused and he was flown back to Addenbrooke's hospital in Cambridge where he received treatment and recovered.
Fourteen years after that, he had pioneering throat reconstruction surgery in London after his condition worsened and he was struggling to eat and breathe.
"I have had a lot of experience of the NHS and the care I received has enabled me to live my life as I want and to contribute to major advances in our understanding of the universe," he will say, referring to his theories on black holes and the origin of the Universe.
His speech is then expected to list some of the developments in the NHS that concern him, including the move towards what he calls a "US-style insurance system".
He will say he believes there has been an increase in private provision of care, including the use of agency staff, that was leading to profit being extracted from the health service.
"The more profit is extracted from the system, the more private monopolies grow and the more expensive healthcare becomes. The NHS must be preserved from commercial interests and protected from those who want to privatise it," he will say.
He will also say that a publicly provided, publicly run system is the "most efficient" and so those who say we cannot afford the NHS are wrong.
"We cannot afford not to have the NHS," he will add.
The speech will also mention Mr Hunt by name, the BBC understands.
In a section about the move towards a seven-day NHS, Prof Hawking will say while he would like there to be more services available at weekends, the government has failed to carry out "proper due diligence", particularly with regard to whether there would be enough staff.
He is expected to quote from a letter he put his name to last year explaining how Mr Hunt "cherry-picked" research to put his case.
But the Department of Health responded by pointing out that the numbers of staff working in the NHS were increasing and it "makes no apology" for tackling the weekend effect.
The statement pointed out that only about 8% of NHS funding goes to the private sector.
It also goes on to point out that "despite being busy", the NHS had been ranked as the "best, safest and most affordable healthcare system out of 11 wealthy nations" in a recent study by the Commonwealth Fund.
"The government is fully committed to a world-class NHS, free at the point of use now and in the future - that's why we're backing it with an extra Â£8bn of investment over the next five years," the statement said.
Stephen Hawking says he is worried about the future of the NHS, attacking the impact of government policies and the health secretary in person.