The populist nationalist reportedly told his supporters: "This Leonardo DiCaprio's a cool guy, isn't he? Giving money for the Amazon to be torched."
Tens of thousands of fires - many of which are believed to have been deliberate - raged through the Amazon over the summer.
Mr Bolsonaro's claims relate to social media accusations that the World Wildlife Fund (WWF) paid for photographs taken by volunteer firefighters to solicit donations.
DiCaprio was said to have made a $300,000 (£230,000) donation.
The four volunteer firefighters accused of being involved were arrested and subsequently released on Thursday following a public outcry.
There appeared to be no evidence to back up the accusations.
DiCaprio has denied having donated to the WWF but voiced his support for "the people of Brazil working to save their natural and cultural heritage".
The actor said: "While worthy of support, we did not fund the organisations targeted."
The WWF's Brazil office also dismissed the claims, saying: "WWF Brazil rejects the attacks on its partners and the lies involving its name, including a series of lie-based social media attacks such as the purchase of photographs linked to a donation from the actor Leonardo DiCaprio."
Earlier this year, DiCaprio's environmental organisation Earth Alliance pledged $5m (£3.9m) to help the rainforest.
Brazil's president has often targeted environmental campaigners and NGOs who have spoken out about protecting the Amazon.
Mr Bolsonaro said in a Facebook live in August that "everything indicates" NGOs were travelling to the Amazon to "set fire" to the forest.
He admitted he had "no written plan" when asked for evidence to back up his claims and later said it could have been farmers setting the forest alight.
In a more recent Facebook live, the Brazilian president said DiCaprio was "collaborating with the burning of the Amazon" as part of an international "campaign against Brazil".
Mr Bolsonaro's son, Eduardo, also claimed on Twitter that the actor had donated to "the NGO that set fire to the Amazon".
Other politicians rejected the claims, with opposition congressman Ivan Valente tweeting: "Bolsonaro's delirium knows no bounds. Accusing Leonardo DiCaprio of paying for the Amazon to be 'torched' is pathetic. But their deliberate lies are also revealing."