The person, named locally as Gareth Williams, 25, of Port Tennant, Swansea, reportedly died at home on Thursday.
The coroner for Swansea, the centre of the epidemic, has ordered an examination of his body to establish whether measles, or another factor, is the cause.
A spokesman for the corner’s office confirmed yesterday that the “unexplained” death of a 25-year-old man is being investigated.
Public Health Wales (PHW) has also confirmed that it is aware that the coroner is investigating a death.
However, confirmation of the cause will not be known until the results of a post mortem examination are released, possibly not until next week.
Neighbours on the Swansea estate where Mr Williams lived in a flat learned of the potential measles link to his death yesterday.
“I think people were under the impression that he died from an asthma attack, that is what I heard,” said one female neighbour, who did not wish to be named.
“He was somebody you rarely saw, to be honest. He often used the back way into his flat so you would not even see him coming or going.
“But it was only when the police and TV cameras turned up that and it was reported on the news that anybody heard anything about measles.”
The death comes as the rate with which the outbreak is spreading continues to grow rapidly with 43 cases in the two days to Thursday.
That brought the headline total, in what is now one of the biggest measles epidemics to hit the UK in a decade, to 808 cases.
PHW director of health protection Dr Marion Lyons said: “Public Health Wales is aware of a death being investigated by the Swansea coroner. A diagnosis of measles has not yet been confirmed.
“Testing the deceased for measles is forming part of the investigations being overseen by the coroner.
She added: “My sympathies are with the family at such a tragic time. Whatever the cause of death in this case, we should not be surprised if, as the outbreak grows, we start to see deaths in Wales.
“Measles is a potentially fatal disease and around one in every 1,000 people who contracts measles in developed countries will die.
“We continue to work to end the current outbreak of measles, which is centred on the Swansea area, and which has now passed 800 cases.”
A Welsh Government spokesman added: “We are aware of a possible death from measles, and extend deepest sympathies to the family and friends at this difficult time.
“We continue to be in close contact with Public Health Wales and to stress the importance of vaccination as the most effective way to protect against measles.”
Special vaccination sessions continue in five schools in the area today and will be extended to 10 schools throughout next week.
Special drop-in vaccination sessions will take place in four hospitals across the region tomorrow for the third consecutive Saturday.
Dr Lyons added: “Those not fully vaccinated with two doses of MMR are highly likely to catch measles, which is highly contagious.
“We know that there are unprotected people in all age groups but we have particular concerns about the 10 to 18 age group. We are therefore urging all parents of children who have missed doses of MMR to arrange vaccination for them as a matter of urgency.
“The MMR vaccine is recommended by the World Health Organisation, UK Department of Health and Public Health Wales as the most effective and safe way to protect children against measles.
“The alarming numbers of cases of measles and continuing spread of the disease in Wales illustrates how vital it is for parents to get their children vaccinated.
“Symptoms of measles include fever, cold-like symptoms, fatigue, conjunctivitis and a distinctive red-brown rash that appears a few days into the illness. Anyone who thinks they or their child may have measles should speak to their GP immediately.”