RNA - Andrey Karlov was attacked while visiting an art exhibition opening in the Turkish capital on Monday, television reports said.
RIA Novosti cited sources as saying that he had died of his injuries.
The Russian Foreign Ministry spokeswoman, Maria Zakharova, had earlier said that he was hospitalized with a gunshot wound.
Moscow said after the assault in Ankara that it was a "terrorist act."
Several other people were also wounded, NTV and CNN-Turk televisions said.
Police fatally shot the assailant. Turkish security sources said he was a police officer working in the Turkish capital.
The ambassador was several minutes into a speech at the embassy-sponsored photo exhibition when a man wearing a suit and tie fired at least eight shots, according to an AP photographer in the audience.
The attacker also said some words in Russian and smashed several of the photos hung for the exhibition.
Turkish authorities stepped security in the area of the fatal shooting.
Melih Gokcek, the mayor of Ankara, said the fatal attack was an attempt to tarnish relations between Turkey and Russia. He made the remarks outside the hospital where the envoy had been taken.
Flashback to downing of Russian jet
On November 24, 2015, Turkey shot down a Russian Su-24 bomber over Syria, killing one of the pilots. The incident marred the bilateral ties, with Moscow insisting on Ankara's apology.
Russia had been conducting combat sorties against Takfiri terrorists since late September 2015 upon a request by the Damascus government.
On June 30, Russia’s President Vladimir Putin said Turkey had apologized to Moscow for the shooting down of the jet. Ankara insisted that it had only expressed regret over the incident.
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