Matt Hancock said that a communication will be sent via text message to people who are classed as vulnerable, setting out specific action for them to take.
The guidelines for people with serious underlying health conditions such as cancer, cystic fibrosis and diseases of body system will ask them stop all social contact for a 12-week period from Monday.
The health secretary said although the new rules were a "really big ask", the new advice was being sent out for "people's own protection".
Speaking to Sky News, he said: “The first thing we’re going to do is set out exactly what conditions that applies to.
“We expect about 1.4 million people to then get a communication from the NHS to say that they are part of this and what they need to do.
“Many of these people have pre-existing health conditions and so will be very worried right now, and I understand that, and they’ll need very specific sets of action – for instance, how do you go about still getting your chemo if you have cancer whilst also social-distancing?
“If you have cancer it’s particularly important to stay away from other people, but you also of course have got to keep going with your chemotherapy.”
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He added: “These are some of the most difficult and challenging cases so we’ll be getting in contact with them, but if people think that they are on this list and don’t receive a communication from the NHS, then they also need to get in contact.
“So that is under way, the money was announced for it yesterday.
“A combination of money to the NHS and money to councils because they’ve got a very big part to play in keeping people safe.”
Entire families or households of more than one person have been told to stay isolated together for 14 days if one of them displays symptoms such as a persistent cough or fever.
Britons who live alone are being told to isolate for at least seven days if they develop a “new and continuous” cough – even “if it is mild”.
New NHS new guidelines, released on Thursday, state: “If you have a high temperature or a new and continuous cough - even if mild, stay at home and follow the specialist medical advice at nhs.uk/coronavirus.
“Only call NHS 111 if you are unable to get online, you have been instructed to do so or your symptoms worsen. Call 999 if you have a life-threatening emergency, make sure you tell the call adviser if you have coronavirus symptoms.”