The president gave no evidence but in the past has accused NGOs critical of his policies of starting fires that ravaged the rainforest this year.
Several arrests have been made amid controversial and unproven allegations fires were started to obtain funding.
DiCaprio, who has pledged $5m for the Amazon, denied Mr Bolsonaro's claim.
The latest comments appear to arise from the arrest of four volunteer firefighters from northern Pará state on allegations they started fires to generate NGO donations.
Rights groups, NGOs and critics claimed the police operation against them was politically motivated and an attempt to harass environmental groups.
Fires that burned in August this year caused global concern for the "lungs of the planet".