The SMS message, purporting to come from the BBC, has been circulating around Asian countries since Monday.
It warns people to take necessary precautions against possible effects of radiation.
The BBC has issued no such flash but the hoax has caused particular panic in the Philippines.
Some media reports suggest that workers and school children there were sent home after the rumours began to spread, prompting the Philippines government to issue an official denial.
Disasters such as that currently unfolding in Japan often trigger a rise in scam texts and e-mails intended to fool users into downloading malware or simply to spread panic.
The US Computer Emergency Readiness Team (US-CERT) has told computer users to be wary of potential e-mail scams, as well as fake anti-virus and phishing attacks regarding the Japan earthquake and the tsunami disasters.
"Such scams may contain links or attachments which direct users to phishing or malware-laden sites," it said.
In the Philippines, the Department of Science and Technology has held a press conference to reassure the public that they are safe even if radiation levels in Japan continue to rise.
On Tuesday morning, reactor 2 at the Fukushima Dai-ichi nuclear plant became the third to explode in four days.
Radiation has reached harmful levels but there is no suggestion that it is affecting anything other than the immediate area.
Officials have extended the danger zone, warning residents within 30km (18 miles) to evacuate or stay indoors.
FAKE E-MAIL IN FULL
BBC Flash news : Japan Government confirms radiation leak at Fukushima nuclear plants. Asian countries should take necessary precautions. If rain comes, remain indoors first 24 hours. Close doors and windows. Swab neck skin with betadine where thyroid area is, radiation hits thyroid first. Take extra precautions. Radiation may hit Philippine at around 4 pm today. If it rains today or in the next few days in Hong Kong. Do not go under the rain. If you get caught out, use an umbrella or raincoat, even if it is only a drizzle. Radioactive particles, which may cause burns, alopecia or even cancer, may be in the rain.
