Moscow has warned that the war games will not disrupt international flights.
The drills come more than two years after a Malaysia Airlines jet was downed over Ukraine during fighting with Russian-backed separatist rebels.
A military source in Crimea told the Reuters news agency: “Warships of the Black Sea Fleet have taken up positions near Crimea's western coast for the duration of Ukraine's planned missile tests from December 1-2.
“The ship's air defence units have been put on a higher state of alert.
“Their equipment is designed in the first instance to shoot down heavy anti-ship missiles and cruise missiles.
"Together with land-based air defence units on the peninsula, the ships have thrown up a practically impenetrable shield against the enemy's rockets.”
Vladimir Krizhanovsky, a Ukrainian military official, earlier said that the exercises had begun and that everything was going smoothly.
He said: “The tests are being carried out in accordance with international law.”
He said they were taking place at least 18.64 miles from Crimean air space.