The patients who contracted the H1N1 virus are 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 bosses said none of the patients are 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 that flu in the community is on the increase.
"And as such, we would therefore expect to see a corresponding rise of cases in hospitals."
Last month, the Evening Times revealed six children were being treated for swine flu at the Royal Hospital for Sick Children at Yorkhill.
Meanwhile, a man died of swine flu in Glasgow's Victoria Infirmary on Monday, February 3.
Colin Campbell, from the Isle of Skye, passed away at the city hospital.
The bug arrived in the UK from Mexico, with the first two cases involving holidaymakers returning to Scotland.
Within days the UK's first person-to-person transmissions was confirmed and the disease began to spread.
During the swine flu pandemic, 1542 people were admitted to hospital in Scotland, and 69 people died.