The defence chiefs are reported to have stepped down in protest at what they see as an attempt by Mr Bolsonaro to exert undue control over the military.
On Monday, the president was forced to reshuffle his cabinet after his foreign and defence ministers both quit.
Mr Bolsonaro's popularity has plummeted over his response to Covid-19.
Brazil's far-right president, who came to power two years ago, has consistently opposed quarantine measures, arguing that the damage to the economy would be worse than the effects of the coronavirus itself.
He has also told Brazilians to "stop whining" about the situation. Nearly 314,000 people have died of Covid-19 in Brazil, with more than 12.5 million confirmed cases.
It is reportedly the first time in Brazilian history that the chiefs of the army, navy and air force have stood down together over a disagreement with the president.
The three men - Gen Edson Leal Pujol, Adm Ilques Barbosa and Lt Brig Antonio Carlos Bermudez - resigned on Tuesday, a day after the president's loyal Foreign Minister Ernesto Araújo was forced to quit following heavy criticism by lawmakers.
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