The airstrikes early Wednesday hit the M1 and M10 hospitals, knocking out generators and cutting off water supplies, putting them temporarily out of service.
Rajab also said two patients died because they could not be kept alive. He says the intensive care unit was severely damaged.
Adham Sahloul, of the Syrian American Medical Society, based in Gaziantep, Turkey, confirmed the strikes and described them as deliberate. He says Assad forces know the location of both facilities.
The closures leave eastern Aleppo with six functioning hospitals, only three of which are capable of dealing with emergencies
Since a ceasefire collapsed last week, opposition-held areas of Aleppo have been heavily bombarded, raising international concern over the plight of their 250,000 residents.