Duda told reporters on Wednesday he had decided to veto the controversial bill due to "many protests and requests from various circles to block these regulations."
"I decided that this is not the right time for us to introduce such solutions," he said, as quoted by public broadcaster Polish Radio’s IAR news agency.
"Today we need unity and agreement; we need to be focused on Poland's security," Duda added, referring to Russia's war against Poland's eastern neighbour Ukraine.
Duda, who is otherwise an ally of Poland's ruling conservative government, had previously indicated that he could use his power to veto the bill.
First Lady Agata Kornhauser-Duda, who is a teacher by professional background, last month met with a group of opposition lawmakers to discuss the bill amid widespread criticism of the proposed new rules.
According to Education Minister Przemysław Czarnek, the bill aimed to "strengthen the right of parents to bring up children in line with their own worldview," while also seeking to help "depoliticize schools and protect children against depravity."
Under the bill, the powers of government-appointed school supervisors would have been extended in a variety of ways, giving the government more authority over school principals, according to state news agency PAP.
Extracurricular activities run by nongovernmental organisations in schools would have required approval from supervisors.
Poland’s ruling conservatives have said the country's education system is in need of regulations to better "protect children from moral corruption."
According to critics, the bill vetoed by the president would have restricted access to teaching on LGBT and reproductive rights, while also giving the governing party greater control over schools.