The patients who contracted the H1N1 virus were being treated at the Glasgow Royal Infirmary.
A spokeswoman for NHS Greater Glasgow and Clyde said "appropriate infection control procedures" are in place.
The statement added: "Any patients who test positive for influenza are isolated or nursed in a designated cohort area until they are no longer symptomatic."
Five years ago a deadly swine flu pandemic broke out and plunged the country into chaos.
Swine flu symptoms include a sudden fever, shortness of breath, a cough and vomiting.
It is a respiratory infection which affects breathing and is caused by a virus that usually affects pigs.
Health chiefs said none of the patients is giving "any cause for concern" as a result of the virus.
Craig Williams, lead infection control doctor, said: "The latest Health Protection Scotland monthly flu report has shown flu in the community is on the increase. As such, we would expect to see a corresponding rise of cases in hospitals."
Last month, it was revealed six children were treated for swine flu at the Royal Hospital for Sick Children at Yorkhill, Glasgow.