The plane was passing over Switzerland carrying members of the Russian delegation and journalists to Lima, Peru for the Asia-Pacific Economic Cooperation (APEC) summit.
Photographs showing the Swiss jets alongside the Russian plane were posted on social media.
"On Friday, November 18, 2016 shortly after 3 pm, two FA/18 planes of the Swiss air force carried out a routine check on a Russian state plane," said the spokesman for the Swiss military, Daniel Reist.
The purpose was "to check the identification of the plane concerned", a procedure he said was "provided for in the rules" of the International Civil Aviation Organisation (ICAO).
Reist noted that the Swiss air force "carries out between 300 and 400 such checks every year".
But Russian authorities expressed surprise at the incident. "We have asked for an explanation from Switzerland concerning the incident involving a Russian government plane in Swiss airspace," the Russian embassy in Bern said in a Twitter message.
It is not the first time that a Russian plane crossing Swiss airspace has been subject to such a procedure. In October 2015, Moscow protested to the Swiss ambassador following a manoeuvre by an F/A-18 near a Russian transport plane carrying a parliamentary delegation to Geneva.
Switzerland apologised, but noted that Russian authorities had received prior notice of the move. The Russian foreign ministry had said it was "unconvinced" by the official Swiss explanation.