The girl, who already suffered from what was described as an "underlying health problem" was being treated at Birmingham Children's Hospital. If her death is confirmed to have been linked to the illness she will become the third Briton to die of the virus.
As news of the death emerged, the Department of Health announced a big jump in the number of patients in England confirmed with swine flu - up 1,604 since Friday, taking the UK total so far to 5,937.
Earlier today, Dr Hamish Meldrum, head of the British Medical Association (BMA), said the public can rely upon doctors to "step up to the mark" as swine flu spreads.
He said flu plans were currently working quite well across the UK, apart from in some areas where NHS trusts thought they could "do better" by departing from national guidance.
Some 366 retired GPs have joined a BMA register, saying they are willing to treat patients if the flu pandemic reaches crisis point.
Dr Meldrum told doctors attending the BMA conference in Liverpool: "As yet, we haven't seen how well the UK will respond to the effects of a full-blown pandemic, but what I can say and where I can reassure the public is that, whatever the crisis, you can rely on the doctors of the UK to step up to the mark."
Elsewhere, six revellers were sent home from the Glastonbury festival over the weekend with suspected swine flu and three or four ball boys and girls suffering from a "flu-like illness" were asked to stay away from the Wimbledon tennis tournament.
However, the West Midlands has seen the highest number of cases, with 2,104 confirmed so far - more than a third of the UK's total and more than two-fifths of all the cases in England.
Last week health officials said the West Midlands, along with London which has 1,564 confirmed cases so far, would adopt a policy of outbreak management, with swine flu cases being clinically diagnosed rather than being confirmed by laboratory results.
The new policy means swabbing will take place only for a small number of cases to keep track of the strength of the virus.
Doctors will also use the drug Tamiflu more selectively, targeting only people with symptoms.
The drug is unlikely to be handed out to everyone who has come into contact with a swine flu sufferer as a precaution.
Chief medical officer Sir Liam Donaldson stressed that many parts of the country were still in the containment phase.
But he warned there could be "tens of thousands of cases" of swine flu each week by the autumn because the virus is more likely to thrive in the colder months.