"The attack happened at 4:00 AM. One warplane targeted both of them directly," said Adham Sahloul of the Syrian American Medical Society (SAMS).
"There are only six hospitals currently operational now that the M2 and M10 have been temporarily taken out of service," he said.
Both hospitals had intensive care units and trauma capacities and had been targeted in previous aerial attacks, according to Sahloul, who described the bombings as "deliberate".
It was unclear if the strikes were executed by Syrian forces or their Russian ally, both of which are carrying out bombing raids in Aleppo city.
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Three employees were injured at the second hospital, among them an ambulance driver, a nurse and an accountant.
"Two patients died. We are still trying to figure out if it was directly because of the attack or because treatment was cut off," Sahloul added.
The two hospitals were put out of commission as Syria's army, backed by Russian firepower, presses an offensive to retake eastern Aleppo city.
Sahloul warned of devastating medical consequences if violence spiked again, as it did with heavy aerial strikes over the weekend, while the hospitals remain closed.
Dozens of people have been killed in heavy bombardment of eastern Aleppo city since Syria's army on Thursday announced an operation to recapture the opposition-held part of the city.
Rights groups have accused Syrian and Russian forces of deliberately targeting medical facilities, with Amnesty International earlier this year accusing the allies of "wiping out hospitals... (as) part of their military strategy.
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