Mr Hancock said he was “incredibly concerned” after it was confirmed the number of fatalities connected to pre-packaged sandwiches and salads provided by The Good Food Chain had risen from three to five.
The affected products have since been withdrawn from hospitals and Public Health England (PHE) said evidence indicated all the deaths had occurred before the items were removed from circulation on 25 May.
PHE said investigations into the outbreak are being carried out in conjunction with the Food Standards Agency (FSA).
Mr Hancock said: “I have been incredibly concerned by this issue and strongly believe that we need a radical new approach to the food that is served in our NHS.
“Staff, patients and families deserve so much better – our NHS should be at the forefront of supporting people to make healthy choices.
“I have instructed the NHS to conduct a root and branch review of hospital food.”
A listeria infection can cause mild symptoms, but in pregnant women and those with a weak immune system it can cause serious problems.
The first three confirmed victims were at Manchester University NHS Foundation Trust and Aintree University Hospital NHS Foundation Trust in Liverpool.
It is not yet known where the latest two victims were receiving treatment, but PHE said there are seven trusts across the country dealing with listeria cases.
One is believed to have died after the first three confirmed cases, while the other died before.
The first case showed symptoms on 25 April and sandwiches and salads were withdrawn on 25 May.
It is understood that some of the products were sold at hospitals while others were given to patients.
The Good Food Chain, which supplied 43 NHS trusts across the UK, voluntarily ceased production.
The business was supplied with meat produced by North Country Cooked Meats, which has since tested positive for the outbreak strain of listeria and also stopped production.
Dr Nick Phin, deputy director at the national infection service at PHE, said: “To date, there have been no patients linked to this incident outside healthcare organisations, but we continue to investigate.”
He told Sky News: “We have identified most of the patients that we think have been affected.
“The outbreak has been pinpointed to this particular brand of sandwiches. They are no longer available and therefore the risk really has been addressed.”
Acknowledging more cases could come to light, he said: “It’s quite possible. The incubation period for listeria can be up to 70 days and given we know that people would have been exposed maybe two or three weeks ago then we just have to wait for the disease to run its course.
“Therefore, it is quite possible we may see one or two cases that have been exposed before the action was taken.”
Dr Phin added: “Most people will present within three weeks. As I say there is a long tail so for one or two people it may be longer.
“Given all the sandwiches were withdrawn on 25 May we are well into the incubation period and that must be extremely reassuring for those involved.”
The Good Food Chain said: “Our thoughts and deepest sympathies are with the families of those who have died and anyone else who has been affected by this outbreak. The underlying cause of it remains unclear.
“For our part, we are co-operating fully and transparently with the FSA (Food Standards Agency) and other authorities, and will continue to do so.”