The EU and US have announced travel bans and asset freezes against a number of officials from Russia and Ukraine.
The moves follow Sunday’s referendum in Crimea, in which officials say 97% of voters backed breaking away from Ukraine and joining Russia.
The individuals targeted by the sanctions are seen as having played a key role in the referendum, which Kiev, the US and EU deem illegal.
Pro-Russian forces have been in control of Crimea since late February.
Moscow says the troops are pro-Russian self-defence forces and not under its direct control.
The crisis follows the ousting on 22 February of Ukraine’s pro-Moscow president Viktor Yanukovych, who had sparked months of street protests by rejecting a planned EU trade deal in favour of closer ties with Moscow.
The EU announced sanctions against 21 officials after a meeting of foreign ministers in Brussels.
Lithuania’s Foreign Minister Linas Linkevic tweeted that further measures were expected to be taken in the next few days.
The US said it had targeted seven top Russian government officials and lawmakers and four Crimea-based separatist leaders with financial sanctions for undermining “democratic processes and institutions in Ukraine”.
The officials include Sergei Aksyonov, the acting leader of Crimea; Dmitry Rogozin, a Russian deputy prime minister; and Valentina Matviyenko, head of the upper house of the Russian parliament.
Monday’s sanctions came hours after Crimea’s parliament declared the region an independent state, following Sunday’s controversial referendum which officials say overwhelmingly backed leaving Ukraine.
The government in Kiev has said it will not recognise the results.
Russia earlier proposed the formation of an international “contact group” to mediate the crisis and seek changes in the constitution that would require Ukraine to uphold military and political neutrality.
But the authorities in Kiev have dismissed the proposal as “absolutely unacceptable”, Ukrainian foreign ministry spokesman Yevhen Perebynis told Interfax Ukraine news agency.
Meanwhile, the parliament in Kiev has formally approved the partial mobilisation of 40,000 reservists and says it is monitoring the situation along the eastern border with Russia.