After meeting with the country's minister of science and technology, Ricardo Galvao said his mandate would be terminated before the end of his term next year due to an "unsustainable" situation.
In recent weeks, Bolsonaro has intensified criticism of INPE deforestation data which has shown a significant increase in illegal logging.
Bolsonaro said at a press conference Thursday that he suspected that agency officials had manipulated figures to make his administration look bad, and he threatened to dismiss those who provided data he deemed "doubtful." Environment Minister Ricardo Salles called INPE's figures sensationalist and inaccurate, but did not offer an alternative estimate.
Since taking office in January, the administration of Bolsonaro has consistently clashed with environmentalists and others over possibly opening up the Amazon rainforest to development and agribusiness.
In a statement Thursday, INPE said it had explained its methodology to government officials at a meeting during which Brazil's environment institute presented its own study that claimed to show "inconsistencies and errors" in INPE's results.
The agency said it had no prior access or knowledge of the study and reaffirmed "its confidence in the quality of the data."
Marina Silva, Brazil's environment minister from 2003 to 2008, said that Galvao had been "fired for his competence, confidence, and for running an institution that did not cower in the face of ...groundless threats."
The World Wide Fund for Nature said it supported Galvao and his defense of "the apolitical and public disclosure of deforestation data."