A second person who had travelled with the woman had "presented some symptoms" and was also "under investigation", the health minister said.
Cyprus is the latest in a string of European countries that have reported cases of H1N1 flu, including Italy, Germany, Norway, Spain, Turkey and the United Kingdom.
The World Health Organisation (WHO) has said that as of May 18, 40 countries worldwide had officially reported 8,829 laboratory-confirmed cases of H1N1 infection.
The US, Mexico, Canada and Japan are among countries reporting the largest number of confirmed cases.
The countries, including the UK and Spain, account for 97.7 per cent of the total number of confirmed cases, the WHO said.
Most of the cases in Europe were human-to-human transmission.
The global death toll has reached at least 99, with Mexcio, where the virus is believed to have originated, accounting for the highest number of these deaths.