In a message posted on her Facebook page on Saturday, Ms Yingluck said, "First I would like to say sorry to every child who wanted to visit Government House, sit in the prime minister's office, take a walk in the compound and participate in different activities.
"But we have to take people's safety into account and I hope that children and their parents will visit other places where there are Children Day's activities."
She said children were the future of the country, like a small light that shines brightly. Thai adults are responsible for making the light shine as brightly as possible and ensuring that children will grow in a friendly society and environment, she said.
She said the slogan for this year's Children's Day was "Be grateful, responsible, virtuous, disciplined, and protect Thailand's stability."
Children's Day activities at Government House were cancelled because anti-government demonstrators, led by the Students and People's Network for Thailand's Reform (SPNTR), continue to occupy nearby areas.
At the protest rally stage on Ratchadamnoen Avenue, the anti-government People's Democratic Reform Committee (PDRC), led by former Democrat Party powerbroker Suthep Thaugsuban, staged its own activities for children on Saturday.
Mr Suthep said his slogan for Thai children was: "Think smart, love the country, love the King, be honest and stay Thai."
The activities at Ratchadamnoen were briefly delayed following a shooting near the rally site early Saturday. Seven people were injured, two critically.