And as the disease has spread from country to country, reports have emerged of people purchasing all sorts of products on the internet.
But while the scramble is understandable, experts are sceptical about just how useful they are.
Professor John Oxford, a virologist at leading London hospital, The Barts and the London, said: "Really, there is very little evidence that masks actually offer much protection against flu.
"I think handing them out to the public as has happened in Mexico just destroys confidence."
Health staff
It is these sorts of issues that has prompted officials from groups such as the World Health Organization and England's Health Protection Agency to steer clear of calling for them for general public use.
While Mexico has handed them out to members of the public, most other countries, including the UK, are just reserving them for health staff.
Others, such as Belgium, have bought some for flu patients, while several, including Spain, have handed them out to passengers on planes returning from affected areas.
It is believed there are enough masks for half the NHS workforce, but officials are already in discussion with suppliers about ordering another 30m to help cope if a pandemic develops.
Health workers have been told to wear them, along with special gloves, if they are in contact with potential victims.
The problem is that when someone sneezes they tend to take a mask off. I think masks give people a false sense of security Dr Ronald Cutler, of the University of London |
"They are the people who will be most likely to be coming into contact with the virus and the ones who could be passing it on."
The Department of Health has focused on getting what are known as respirator masks. These have filters, which stop a person breathing in some particles in the air.
They are much more effective than the standard surgical masks or dust masks that are sometimes used by builders.
However, none of the masks can stop 100% of the particles getting through and become less effective once they become moist.
Instead, they are better at stopping the virus getting out.
Spread
Dr Ronald Cutler, deputy director of biomedical science at the University of London, said: "If you sneeze with a mask the virus will be contained so from that point of view if everyone wore them it might stop the spread.
"Or you could get the people with flu wearing them, but by the time they are diagnosed it could be too late.
"And the problem is that when someone sneezes they tend to take a mask off. I think masks give people a false sense of security.
"They are not bio-chemical suits. Masks are obviously just covering one part of the body so your hands and clothes could all have the virus on and when you take them off you will infect yourself.
"However, because people are wearing a mask they will think they are protected and may go into crowded areas.
"The best advice is to wash your hands and cover your mouth when sneezing."
Gail Lusardi, an infection control specialist at Glamorgan University, agreed.
"Masks alone will not prevent spread of the influenza virus and basic hygiene measures like hand washing, safe use and disposal of tissues and cleaning of environmental surfaces are key to preventing infection transmission."
She also said it was important they were correctly fitted - some of the more expensive respirator masks are molded to fit the face unlike standard masks that can be bought on the high street.
And she added: "A mask can be worn continuously for up to eight to 10 hours, but must be replaced if it is taken off at any stage."
http://news.bbc.co.uk/2/hi/health/8024605.stm