According to Public Health England (PHE), the death is one of nine cases previously confirmed, and there have not been any new cases linked to the outbreak.
The patient, whose age and gender were not given, got listeriosis from Good Food Chain products while at Western Sussex Hospitals NHS Foundation Trust.
The Good Food Chain products - now in liquidation - supplied 43 NHS trusts with prepackaged food.
However, the Food Standards Agency previously confirmed that the company was not the source of the outbreak.
Inquests have opened for three of the victims of the outbreak.
Western Sussex Hospitals’ chief nurse and director of infection prevention and control, Dr Maggie Davies, said they were "greatly saddened by this news and wish to extend our sincere condolences to the patient’s family and friends.
“Patient safety is always our absolute priority and as soon as we were informed we may have received contaminated chicken sandwiches from the Good Food Chain we removed all products from our hospitals.
“Since then, we have had no further listeriosis infections reported to us and we want to reassure our patients, visitors and staff that the risk remains very low.”
PHE said it was testing all samples of listeria on an ongoing basis.
It has tested 34 samples of listeria and said that none are linked to the outbreak.
The other deaths occurred at four different hospital trusts.
Enid Heap, 84, died at Manchester Royal Infirmary on May 6 with her family at her bedside, Manchester Coroner’s Court heard in June.
The “linked death” of Beverley Sowah, 57, who was born in Jamaica and lived in Manchester, is also being investigated, senior coroner Nigel Meadows said.
A separate inquest into the death of Ian Hitchcock, 52, also opened at Derby Coroner’s Court.
The businessman died after eating a contaminated sandwich while at the Royal Derby Hospital.
There is another case at Western Sussex Hospitals NHS Foundation Trust, one case at Frimley Health NHS Foundation Trust and one at East Kent Hospitals University NHS Foundation Trust, which have not been fatal.
The Good Food Chain, which supplied 43 NHS trusts across the UK as well as one independent provider, voluntarily ceased production and PHE said the investigation into the outbreak is continuing.
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.
Listeria infection is rare and usually causes a mild illness in healthy people.
However, it can have more serious consequences among those with pre-existing medical conditions, pregnant women and those with a weak immune system.
PHE insisted the health risk to the public remains low.