The youngsters who contracted the H1N1 virus were treated at the Royal Hospital for Sick Children at Yorkhill.
A spokeswoman for NHS Greater Glasgow and Clyde said the six cases were not connected to each other.
She added: "The number of children with seasonal flu is currently what you would expect for this time of year, including H1N1, which is prevalent in the community.
"There is no outbreak.
"Six individual cases with no connection have been admitted to the Royal Hospital for Sick Children over the last two weeks, which is consistent with expected rates."
However, earlier this month, a ward at a Leicester hospital where six children were diagnosed with swine flu was intensively cleaned in a bid to prevent further outbreaks.
The children were diagnosed with the H1N1 virus at Leicester Royal Infirmary and were treated separately from other patients.
All six children were diagnosed with the condition on February 14.
The University of Leicester Hospitals NHS Trust also said it had vaccinated as many front-line staff as possible against the swine flu virus.
Nearly five years ago a deadly swine flu pandemic broke out and plunged the country into chaos.
Last month, a six-year-old boy from Belfast became unwell and was admitted to the Royal Belfast Hospital for Sick Children.
He was later transferred to Yorkhill Hospital.
As reported by the Evening Times earlier this month, a man died of swine flu in Glasgow's Victoria Infirmary.
Colin Campbell, from the Isle of Skye, passed away on Monday February 3.
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.
Five years ago, the bug arrived 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.
The majority of deaths occurred in the NHS Greater Glasgow and Clyde area.