Just 45% of young children have been vaccinated since the Scottish Government extended its seasonal flu programme to include two and three-year-olds on October 1.
Scotland's Chief Medical Officer, Sir Harry Burns, said: "Every year we see examples of how devastating flu can be for children, particularly the youngest ones who have little immunity to the infection. In fact, youngsters are two to three times as likely to be ill with flu than adults."
A couple whose daughter was hospitalised when she contracted flu urged other parents to get their children vaccinated.
Alison and Dan Flowers, 35, of Edinburgh, were devastated when their daughter Millie, aged two, was admitted to a children's hospital twice due to complications from flu. Millie was left severely unwell after contracting the viral illness.
They hope that their story will encourage parents of young children to take advantage of the Scottish Government's flu programme, which now includes two and three-year-olds.
Mrs Flowers said: "You just don't know how flu will affect your children, and it can often be a great deal more harmful to youngsters than adults as they haven't built up their immunity.
"Flu caused Millie to be severely ill and I would never want her to go through such intense pain and distress again.
"I ensured that she received her vaccination as soon as possible this year, and she is now perfectly healthy."
The extension is the first stage in the government's longer-term plan to offer protection against flu to everyone aged between two and 17 over the next few years.
Fluenz, the vaccine used for children, is administered as a nasal spray. It offers protection for around 12 months.
People aged 65 and over, pregnant women, unpaid carers, those undergoing chemotherapy and healthcare workers are also able to receive a free vaccine.
Sir Harry added: "Flu strikes suddenly and it's important for both adults and children to be prepared. The extension of the flu vaccination programme will not only protect children but it will also help prevent the spread of the flu virus."