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.
US President Barack Obama said in a press conference that Washington stood "ready to impose further sanctions" depending on whether Russia escalated or de-escalated the situation in Ukraine.
If Moscow continued to intervene in Ukraine, he warned, it would "achieve nothing except to further isolate Russia and diminish its place in the world".
The EU published a list of sanctions against 21 Russian and Ukrainian officials after a meeting of foreign ministers in Brussels. The list includes the acting prime minister of Crimea, the speaker of Crimea's parliament, three senior Russian commanders and several senior Russian parliamentary officials.
"We regret that Russia has so far not engaged in negotiations with Ukraine," EU foreign policy chief Catherine Ashton said in a press conference after the sanctions were announced.
UK Foreign Secretary William Hague told reporters the list was not "set in stone".
He said this depends on "how Russia reacts to the referendum in Crimea which has been a mockery of any real democracy, and how they are reacting to the possibility of discussions and direct negotiations with Ukraine over the coming 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 US list included Dmitry Rogozin, a Russian deputy prime minister, Valentina Matviyenko, head of the upper house of the Russian parliament and the ousted Ukrainian leader, Viktor Yanukovych.
"Today's actions send a strong message to the Russian government that there are consequences for their actions that violate the sovereignty and territorial integrity of Ukraine, including their actions supporting the illegal referendum for Crimean separation,'' the White House said in a statement.
The EU has also shown its support for Ukraine by announcing it will temporarily remove customs duties on Ukrainian exports to the EU.
Ukraine's acting President Oleksander Turchinov said Kiev was ready for negotiations with Russia, but it would never accept the annexation of Crimea.
In a televised address, Mr Turchinov said that any actions inciting mass disorder would be viewed as "abetting the military aggressor and a crime against the state".
The Kiev authorities earlier said they had recalled their ambassador to Moscow for consultation.
Ukrainian Foreign Minister Andriy Deshchytsya has welcomed the EU's decision to impose sanctions.
He told the BBC: "I think it's a step forward in mobilising the international community and confronting the Russian decision to violate international order and international laws. Crimea is an integral part of Ukraine."
Russian Deputy Prime Minister Dmitry Rogozin, who is on the US sanctions list, says the measures will not affect those who do not have assets abroad, Reuters reports
"Comrade Obama, and what will you do with those who have neither accounts nor property abroad? Or didn't you think of that?" Mr Rogozin wrote on Twitter.
Monday's sanctions came hours after Crimea's parliament declared the region an independent state, following Sunday's referendum.
According to the parliamentary vote, Ukrainian laws now no longer apply in the region, and all Ukrainian state property belongs to an independent Crimea.
The peninsula will adopt the Russian currency, the rouble, and clocks will move two hours forward to Moscow time by the end of March.
The document approved by MPs also appealed to "all countries of the world" to recognise Crimean independence.
The government in Kiev has said it will not recognise the results of the referendum.
Russia earlier proposed the formation of an international "contact group" to mediate in 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.