Mr Queiroga, who had received a COVID-19 vaccine, was the second member of Mr Bolsonaro's entourage to test positive for the virus since arriving in New York.
The 55-year-old health minister will remain in the United States for a period of isolation, even though the rest of the delegation has returned to Brazil.
Mr Bolsonaro, who appeared without a mask on several occasions during the trip, has not been vaccinated and repeated that he would be "the last" Brazilian to receive the vaccine.
Mr Queiroga was with Mr Bolsonaro, who last year survived a bout of the virus, at several events, including a meeting with British Prime Minister Boris Johnson on Monday.
He was "doing well," the statement said.
He wrote on Twitter that while following "all health security protocols", the ministry "will continue to take firm action to deal with the pandemic in Brazil".
Mr Bolsonaro caused a stir on social media after a photograph showed him taking few precautions against contagion while around others in his delegation, as he ate a slice of pizza from a New York street vendor.
The health minister was the only one in the photo wearing a mask, but he had pulled it down under his chin.
Under fire for his controversial handling of the pandemic, which has claimed more than 591,000 lives in Brazil, Mr Bolsonaro opened the General Assembly with a speech in which he made several misleading or inaccurate statements, some of which related to the pandemic, according to AFP’s Factcheck team.