The developments were a blow to Russia, which has been one of the staunchest supporters of Syrian President Bashar Assad in his country's bitter civil war, now in its sixth year.
The shelling that killed the female nurse also wounded two Russian doctors working in the field hospital, a Russian officer in Aleppo told reporters.
In Moscow, Defense Ministry spokesman Maj Gen Igor Konashenkov confirmed the death of one Russian medic in Aleppo and said two were seriously wounded in an artillery attack that hit the Russian military hospital.
He said an unspecified number of local residents who were at the hospital were also wounded and accused the United States, Britain and France of tipping off the rebels about the hospital's location.
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Separately, the Defense Ministry said a Russian Su-33 fighter jet, based on the aircraft carrier Admiral Kuznetsov, crashed into the Mediterranean Sea after returning from a sortie over Syria. The ministry said that "because of the failure of the arrester system's cable, the Su-33 fighter rolled off the deck" today.
The pilot successfully ejected and was unharmed, the ministry said, adding that Russian military operations over Syria would not be affected by the incident.
In Aleppo, rebel shelling on the government-held part of the contested city has intensified in recent weeks as Syrian government and allied troops push their way into parts of Aleppo controlled by the opposition.
In an offensive that began last week, Syrian government forces seized large swaths of the Aleppo enclave that have been under rebel control since 2012.
The fighting was most intense today near the dividing line between east and west Aleppo as government and allied troops pushed their way from the eastern flank, reaching within less than 1 kilometer from the citadel in the center of the city.