Washington has said it had supplied the arms to Ukraine, which has been asking for more powerful weapons for months as it struggles to contain advancing Russian forces.
Moscow's defence ministry said it had destroyed six Army Tactical Missile System (ATACMS) rockets "in the last 24 hours", without saying where they were shot down.
The Russian-installed head of Crimea, Sergei Aksyonov, said one of the missiles was downed in the village of Donskoye, outside the main city of Simferopol.
"After an ATACMS missile was shot down, undetonated submunitions scattered," Aksyonov said on Telegram.
"If you find such a weapon, do not pick it up or come close and call emergency services or the police," he warned.
Aksyonov posted a photograph of a metal ball which he said was part of the destroyed missile.
Russia did not say if the missiles caused any damage in Crimea.
Earlier, an official from Russian-occupied southern Ukraine, Vladimir Rogov, said that air defence had been in operation over Simferopol and the town of Dzankoi, in northern Crimea.
Ukraine has regularly attacked Crimea during Moscow's more than two-year offensive.
But it did not comment on Tuesday's attack.
Last week, the United States said it had sent ATACMS missiles to Ukraine in February.
Ukrainian forces are now awaiting the arrival of new US weapons, green-lighted by President Joe Biden after months of being blocked by political wrangling in Congress.
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