According to El Pais newspaper, the NATO fighter belongs to Spain and has been in Lithuania since May 2 as part of a NATO mission.
A NATO official has earlier confirmed to Sputnik that the alliance's jets were scrambled on Tuesday to identify a Russian aircraft that closely approached the allied airspace.
The Russian Defence Ministry said on Tuesday that a NATO F-18 combat jet approached Shoigu's aircraft and was forced away by two Russian Su-27 fighters.
Tuesday's incident wasn't the first time NATO aircraft have approached Shoigu's plane in the Baltic. A similar incident took place in June 2017, when a NATO F-16 was nudged away from the plane by a Su-27 escort.
The US and its allies have substantially increased flights along Russia's maritime and land borders in the Baltic and Black Sea regions, and near Russian bases in Syria. In 2018, the Defence Ministry reported observing some 3,000 foreign military aircraft, including about 1,000 reconnaisance planes and drones, flying near the border. Some of these incidents prompted air defence forces to scramble jets. Russia has repeatedly condemned the NATO military buildup near its borders, warning that these actions increase the risk of escalation into a full-blown military conflict.