Bolsonaro, 70, was taken from prison to hospital in Brasilia early on Friday with a high fever, chills and a drop in oxygen saturation, the note said, adding that he is being treated with antibiotics.
His condition is serious and he is expected to remain in hospital for at least the next few days, one of the doctors treating him, Brasil Caiado, told reporters in Brasilia.
Surgery has been ruled out for now, Caiado said.
Bronchopneumonia is a lung infection that spreads from the airways into the lungs, posing problems such as breathing difficulties.
Bolsonaro is serving a 27-year sentence for plotting a coup after losing the 2022 presidential election to current President Luiz Inacio Lula da Silva.
The Bolsonaro family and his lawyers have called for him to be placed under house arrest since he was jailed in 2025. Justice Alexandre de Moraes, who oversees the case, has denied previous petitions, with a panel at the court upholding his decision.
"Jair Bolsonaro's life is being deliberately put at risk," his eldest son, Senator Flavio Bolsonaro, said on X, adding, "there is no longer any justification" for not placing Bolsonaro under humanitarian house arrest.
The senator has announced himself as a prospective candidate in Brazil's 2026 presidential election, to be held in October. In the past week, at least two public opinion polls showed he and Lula statistically tied in a potential second-round match-up.
Former president Bolsonaro, who governed from 2019 to 2022, has a history of hospitalisations and surgeries related to a stabbing during a 2018 campaign event.
He had been in hospital in January for a series of exams after falling and hitting his head. In December, he underwent medical procedures to treat a hernia and persistent hiccups. Moraes has said Bolsonaro, who in January was transferred to a prison with a larger cell, can be treated in prison. The justice has also mentioned a flight risk in previous denials.
Bolsonaro was imprisoned in November after he took a soldering iron to his ankle monitor. The former president had been wearing the device during house arrest while he appealed the coup plot conviction, which was later confirmed.
Bolsonaro has denied he plotted a coup. He has blamed hiccup medications for his tampering with the ankle monitor in November.
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