"Now the territory [of the embassy] is cordoned off, sappers are working," the source said.
The embassy's press service is not yet available for comments.
The Bishkek police said that a bomb threat had also been received by the embassy of China, also on Tuesday morning, but neither turned out credible.
"Search operations did not find any explosive substances or devices in the embassies of Russia and China," a spokesman for the police said.
The search involved police officers, sappers and K9 officers, the spokesman said. False bomb threats are punishable in Kyrgyzstan by up to three years in prison.