The Welsh Assembly Government confirmed the woman from Caerphilly County Borough died on Saturday following further circulatory complications.
There have been more than 50 swine flu-related deaths in the UK so far.
Wales' Health Minister Edwina Hart said there was no increase in case rates in Wales.
The woman was first admitted to the Royal Gwent Hospital in Newport where she tested positive for swine flu on admission and received a course of antivirals.
She was later transferred to the intensive care unit at the University Hospital of Wales in Cardiff.
Ms Hart said: "This is the first swine flu-related death in Wales and I would like to send my condolences to the family and friends of the woman at this difficult time.
SWINE FLU ADVICE If you have symptoms, stay home and check out the symptoms on NHS Direct Wales Or phone the swine flu information line on 0800 1 513 513 for recorded advice and informationMost people will not need further advice and support and can self-medicate at home with rest, plenty of fluid and paracetamolIf you are in an at risk group or your symptoms get worse call your GPIf people contact the National Pandemic Flu Service - either the website or the call centre - they will be directed to contact their GPSource: Welsh Assembly Government "Tragic though this is for the family and friends, we are not seeing an increase in rates of cases, compared to normal seasonal flu, where we see a number of serious cases and deaths each year."
The chief medical officer for Wales, Dr Tony Jewell said there had been more than 50 swine flu-related deaths in the UK since the flu pandemic arose in April.
"I understand that the first death of someone with swine flu in Wales will naturally worry people and cause concern, however I would assure people that for the vast majority of healthy people, the infection remains mild and people recover within five to seven days with rest, plenty of fluids and symptomatic treatments," he added.
"People with underlying health conditions, especially heart and lung diseases, are at most risk.
"Even in the at risk groups - those with chronic conditions, pregnant women and children under five - most people get over the infection with no major concerns.
"If people are concerned, or if they are in these at risk groups, they should contact their GP or NHS Direct Wales.
"Antivirals have the most impact within 48 hours of the onset of flu-like symptoms."
NHS Direct can be contacted on 0845 4647.