"Tragic though today's death is, I would like to emphasise that the vast majority of those who have H1N1 are suffering from relatively mild symptoms," she said.
Scotland has confirmed 498 H1N1 cases out of a British total of 1,261 - the highest in Europe.
The World Health Organisation (WHO) declared an influenza pandemic on Thursday and advised governments to prepare for a long-term battle against the virus.
The WHO said last week that the virus has not become any more lethal, but is now unstoppable with health authorities expecting to see more cases and deaths worldwide.
"If your lungs are already only working at half capacity when the virus kicks in and takes half of what is left, you will be left teetering on the edge"
However, H1N1 appears to be a relatively mild virus, and most people who have contracted it have not need treatment to get better.
About half the people who have died from the flu virus have had other health conditions including pregnancy, obesity, diabetes, or asthma.
Hugh Pennington, a bacteriologist at Aberdeen University in Scotland, said the underlying conditions were likely to have been a "significant factor'' in the death in Scotland because they raise the odds that the patient will have difficulties.
"It makes it more likely that they will get the serious form of the virus in the first place,'' he said.
"If your lungs are already only working at half capacity when the virus kicks in and takes half of what is left, you will be left teetering on the edge.''
Pennington said that while the death was unfortunate, it was "quite unremarkable'' given the number of reported cases and compared favorably to ordinary seasonal flu.
Most of the global flu deaths have occurred in Mexico, where the virus was first detected, while the United States has the highest number of cases with more than 13,000 people infected.