A Russian Sukhoi-27 fighter jet was then seen inserting itself between the F-16 and the minister's plane before tilting its wings from side to side to show the missiles it is carrying.
According to the Pentagon, spokesman Captain Jeff Davis said the USA aircraft "did nothing to provoke this behavior" and that the Russian jet was flying dangerously.
Two Russian Su-27 warplanes chased away a North Atlantic Treaty Organisation F-16 jet over neutral waters in the Baltic Sea.
Speaking to Sputnik, Russian experts share their views on the incident and its potential implications. A Russian fighter jet intercepted a small group of United States warplanes, including Boeing KC-135 Stratotanker military refueling aircraft, two B-1 bombers and one B-52, during the BALTOPS (Baltic Operations) annual training exercise on June 10.
However, Pentagon spokesman Jeff Davis denied the Russian accusation, saying "We were operating in worldwide airspace and did nothing to provoke this behavior".
The Russian Defense Ministry argued that "all flights of Russian interceptors over worldwide waters of the Baltic Sea are carried out strictly in accordance with global rules". The Russian reports did not indicate which nation was flying the North Atlantic Treaty Organisation warplane.
So who at North Atlantic Treaty Organisation wants to take responsibility for this one?
When asked by CNN if the North Atlantic Treaty Organisation jet was chased away, the official said: "Once identification of the aircraft was complete, our jets broke away as it is standard procedure".
Also on Tuesday, a USA fighter jet shot down a second drone belonging to the Syrian regime in a month. "We assess the Russian pilots' behaviour as safe and professional".
Kaliningrad, Mr Shoigu's destination, is a highly militarised Russian enclave on the Baltic.
"Our air crew are trained to handle these types of intercepts, and it appears that the Russian air crew are trained to conduct them", Lt. Gen. Richard Clark, 3rd Air Force commander, told reporters last week.
Tensions between the airforces of the two nations have increased after Moscow said it would treat any plane with the US-led coalition in Syria that flew west of the Euphrates as a potential target.
Russian Federation has previously threatened to take military action in response to USA attacks on its allies elsewhere in Syria.
"Apart from using political, information and economic pressure, some countries also seek to employ military force in order to achieve their political goals", Shoigu said, according to state media.
These were hardly the only instances where North Atlantic Treaty Organisation and Russian warplanes have met over the Baltic Sea in recent weeks. Russian and North Atlantic Treaty Organisation jets have buzzed each other in the past, but this is the most high profile incident to date.