It was not immediately clear who was in control of the buildings but a Reuters correspondent on the scene said the Russian flag was flying over both in the regional capital, Simferopol.
Ethnic Tatars who support Ukraine's new leaders and pro-Russia separatists had confronted each other outside the regional parliament on Wednesday.
Interfax quoted a local Tatar leader, Refat Chubarov, as saying on Facebook: "I have been told that the buildings of parliament and the council of ministers have been occupied by armed men in uniforms that do not bear any recognisable insignia."
"They have not yet made any demands," he said.
About 100 police were gathered in front of the parliament building. Doors into the building appeared to have been blocked by wooden crates.
The streets around the parliament were mostly empty apart from people going to work.
"I heard gunfire in the night, came down and saw lots of people going in. Some then left. I'm not sure how many are still in there," said a 30-year-old man who gave his name only as Roman.
Ukrainian President Viktor Yanukovich was ousted on Saturday after three months of unrest led by protesters in Kiev.
He is now on the run being sought by the new authorities for murder in connection with the deaths of around 100 people during the conflict.
Crimea was transferred from Russia to Ukraine in 1954 in the Soviet-era by then Soviet leader Nikita Khrushchev.
With a part of Russia's Black Sea fleet based in the port of Sevastopol, it is the only region of Ukraine where ethnic Russians dominate in numbers, although many ethnic Ukrainians in other eastern areas speak Russian as their first language.
With Crimea now the last big bastion of opposition to the new post-Yanukovich political order in Kiev, Ukraine's new leaders have been voicing alarm over signs of separatism there.
The Tatars, a Turkic ethnic group, were victimised by Soviet dictator Josef Stalin in World War Two and deported en masse to Soviet Central Asia in 1944 on suspicion of collaborating with Nazi Germany.
Tens of thousands of them returned to their homeland after Ukraine gained independence with the collapse of the Soviet Union at the end of 1991.