The move came as Crimea held a referendum on Sunday on joining Russia. According to the officials, 97% of voters backed breaking away from Ukraine and joining Russia.
The so-far unnamed individuals targeted by the sanctions are seen as having played a key role in the referendum, which Kiev, the US and EU claim illegal.
The crisis follows the ousting on 22 February of Ukraine's President Viktor Yanukovych, who had sparked months of street protests by rejecting a planned EU trade deal in favor of closer ties with Moscow.
The EU announced its new sanctions 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.
Monday's sanctions came hours after Crimea's parliament declared the region an independent state, following Sunday's referendum which overwhelmingly backed leaving Ukraine.
RA/NJF