The ministry described the four-day practice - ordered by President Vladimir Putin - as a "massive surprise inspection" to check combat readiness.
It comes as one of Putin`s closest aides, Deputy Prime Minister Dmitry Rogozin, issued a chilling warning to the West.
He said: "It is our territory, it is our shelf, and we`ll provide its security. And we will make money there.
"I have always joked about it, that they will not give us visas.
"They will put us on a sanctions list - but tanks do not need visas."
It is the third major military exercise staged by the Kremlin in the past three months.
The tests also began on the same day as Nato and some of its partners started an Arctic training exercise.
Russia`s actions in Ukraine and incursions into Western airspace have led to rising tensions with the West.
According to reports on the Russian agencies Interfax and Tass, the inspection of the aviation group and air defence forces in the central military district involves almost 700 weapons and pieces of military hardware.
During the exercise, Russia`s long-range aircraft are due to carry out cruise missile strikes on practice targets in the Komi republic.
The outspoken politician is himself on EU and US blacklists as part of sanctions following Russia`s annexation of Crimea last year, limiting his travel options.
Russia has been heavily criticised in recent months over increased air activity around the Nordic countries, including several airspace violations by military aircraft.
Nato`s two-week training exercise in the region - which began on the same day as Russia`s tests - will be based in the north of Norway, Sweden and Finland. It will involve 115 fighter planes and 3,600 troops from nine countries.
The Arctic Challenge Exercise will also involve troops and planes from the US, Britain, Germany, France and the Netherlands - all Nato members - as well as neutral Switzerland.
The exercise is the second of its kind, following similar tests in 2013.
The defence ministers of Norway, Sweden, Finland and Denmark, along with Iceland`s foreign minister, signed a joint declaration in April in which they called Russia`s military aggression "the biggest challenge to European security".
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