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.
Chief medical officer Sir Harry Burns said: "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.
"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.
"The vaccine that will be used for most children is called Fluenz and is administered as a nasal spray rather than an injection. The flu vaccine only takes a few minutes, but will offer protection for around 12 months. Before we move any deeper into winter, I encourage all parents to take their toddler for the flu vaccination."
Alison Flower, 35, saw her two-year-old daughter Millie spend three nights in Edinburgh's Sick Kids' hospital with complications from the flu virus in March.
She 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. We are able to enjoy the Christmas festivities as a family.
"It was so worrying seeing our child so ill in hospital. No-one would want to go through this ordeal, and I strongly advise all eligible parents to ensure that their toddler receives the vaccination, to offer protection from the flu virus this winter."