Bolsonaro, who has bragged about not being vaccinated himself and has consistently cast doubt on the efficacy and safety of coronavirus vaccines, said in a radio interview he had not heard of children dying of COVID-19 and repeated that his daughter Laura, 11, would not be getting vaccinated.
Bolsonaro said vaccines could have side effects on children, but gave no evidence.
Brazil's health regulator Anvisa, and authorities around the world, have found COVID-19 vaccines are safe for those aged five and above.
"Are you going to vaccinate your child when the possibility of dying is almost zero? What is behind this? What are the interests of vaccine maniacs?" Bolsonaro said.
The Ministry of Health announced on Wednesday it had bought 20 million children's vaccines developed by Pfizer, and voluntary vaccination of five to 11-year-olds would begin by the end of the month.
In a social media broadcast later on Thursday, Bolsonaro stressed the vaccination was not obligatory.
"No town mayor or state governor can prevent a child from going to school for not being vaccinated," he said.
Bolsonaro warned Pfizer has not assumed responsibility for any side effects the vaccine could have in children, and said parents should immediately seek a doctor if their child developed chest pains or shortage of breath.
The Brazilian Society of Pediatrics rejected that view and said in a statement Brazilians should fear the virus and not the vaccines, which can save lives at any age.
Anvisa approved the Pfizer vaccine for children on December 16, drawing heated criticism from people opposed to vaccines and the president, who suggested children only be vaccinated with a doctor's prescription.
The ministry dropped the idea as impractical.
According to the national council of state health secretaries, at least 300 children aged five to 11 had died with COVID-19 in Brazil by the start of December.
Brazil's army this week differed from the president on how to deal with COVID-19.
It ordered soldiers to get vaccinated, wear masks and maintain social distance, and warned them against spreading false information about the pandemic.
