Among the hacked sites were those of the presidential administration and the central bank, the state-backed Russian news agency RIA Novosti said.
"A powerful attack on the site is ongoing," a government spokesman said. "Measures are being taken to restore the normal functioning of the site."
Bank of Russia said in a statement its website was dark for about an hour following a denial of service attack.
The origin of the attack was not immediately known, RIA Novosti said. However, officials at the central bank said that hack was thought to be linked to the Islamic anti-Russian group Anonymous Caucasus.