"It is related to the growing military activity of North Atlantic Treaty Organisation countries in Eastern Europe", Shoigu said.
A week ago, the Defense Ministry reported 18 such incidents.
The NATO jet closed in and began flying parallel to Shoigu's plane, video shot on board and released by the Defense Ministry's Zvezda news agency showed.
Shoigu was on his way to Kaliningrad, a highly militarised Russian exclave on the Baltic Sea, to take part in a meeting with defence officials there.
The bulk of those flights was performed by United States' RC-135 jets and RQ-4B Global Hawk drones, which approached Russian borders 10 times in total.
However, Russia disputes these claims, saying the US Air Force RC-135 aircraft made a "provocative" move towards their Su-27 fighter jet as it intercepted two American planes "flying towards the Russian state border".
A Russian Su-27 fighter accompanying Shoigu's plane then approached from behind and rocked its wings to show that it was armed.
The Baltic region has become a hotspot for Russia-NATO confrontation as the US -led alliance is increasing its military presence in the area near the Russian border. The vast majority of these encounters have been safe and professional, the official added - a point that adds to the significance of Monday's incident.
Pentagon Spokesman Captain Jeff Davis told reporters: "We were flying in worldwide airspace and did nothing to provoke this behavior".
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.
He said the situation in Russia's western borders "tends to deteriorate" because of North Atlantic Treaty Organisation.
Earlier this month, the US Air Force deployed 800 troops and long range B-52 bombers to the United Kingdom to take part in joint North Atlantic Treaty Organisation exercises.
North Atlantic Treaty Organisation confirmed the intercept, saying in an emailed statement that "three Russian aircraft, including two fighters", had been tracked over the Baltic Sea.
The meeting came after North Atlantic Treaty Organisation held military exercises at the weekend in Poland on the Lithuanian border close to Kaliningrad.