Video shot from Shoigu's plane shows a Russian Su-27 fighter then flying between the North Atlantic Treaty Organisation jet and the foreign minister.
Shoigu was en route to the westernmost Russian city of Kaliningrad when the F-16 attempted to make an approach.
A North Atlantic Treaty Organisation fighter jet tried to approach Mr Shoigu's plane but a Russian escort plane intervened to defend it, Interfax news agency reported, citing journalists accompanying the minister.
Earlier this month, Russian Federation scrambled a fighter jet to intercept a nuclear-capable U.S. B-52 strategic bomber it said was flying over the Baltic near its border, in an incident that had echoes of the Cold War. The altercation lasted just a few minutes before a Russian SU-27 drove the North Atlantic Treaty Organisation plane away. The defense minister said this is demonstrated by the ongoing Baltops and Saber Strike military drills, which involve thousands of troops as well as dozens of military planes and ships.
However, the Russian Ministry of Defense offered a different version of Monday's incident.
Since June 2 there have been more than 35 interactions in the Baltic Sea region between US and Russian jets and warships.
The Russian plane was armed and flew "erratically", a U.S. official told CNN, noting that the maneuvers were deemed unsafe due in part to the proximity of the aircraft. The F-16 then distanced itself from the Russian planes.
The U.S. military command overseeing operations in Europe released photos Friday of a June 19 close encounter between a U.S. RC-135U reconnaissance aircraft and a Russian SU-27 fighter in global airspace over the Baltic Sea.
He said the situation in Russia's western borders "tends to deteriorate" because of North Atlantic Treaty Organisation.
An armed Russian SU-27 Flanker confronts a U.S. RC135U.
There have been a series of confrontations between North Atlantic Treaty Organisation allies and Russian Federation in the Baltic Sea in recent weeks.
Russia, a staunch ally of Syrian President Bashar al-Assad, said it would treat US-led coalition aircraft flying west of the Euphrates River in Syria as potential targets and track them with missile systems and military aircraft.
Shoigu suggested NATO's activities has led Russian Federation to increase its military capacity in response.