Sergei Shoigu told a meeting of defence ministry top brass it was a "priority" to deploy a "full and self-reliant group of troops in the direction of Crimea," Russian news agencies reported.
He said the "situation in Ukraine has sharply worsened and the foreign military presence has increased very close to our border".
Shoigu said the "military and political situation" in southwest Russia had "changed significantly since the start of this year."
NATO this month agreed to set up a new rapid response force that would be ready to deploy within a few days and also to maintain a "continuous presence" in its eastern member states.
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Putin said last month that it was necessary to "implement all of the country's defence measures fully and promptly, including of course in Crimea and Sevastopol, where we have to de facto create military infrastructure from scratch".
Putin ordered the annexation of Crimea from Ukraine in March, saying later he had righted a wrong by reclaiming a peninsula that used to belong to the Soviet republic of Russia before 1954.
Over the weekend Crimea's residents joined Russians across the country in voting in the first local elections since the peninsula's takeover.
In Sunday's elections to the Crimean regional parliament, Russia's ruling United Russia party won more than 70 per cent of the vote, while the ultra-nationalist Liberal Democratic Party of Russia received just under 8.5 per cent.
The United States yesterday rejected the Crimean polls as illegitimate.