"We will restrict entry to Canada for key Ukrainian government officials that have been responsible for the repression and silencing of opposition voices," Alexander told a news conference in the foyer of the House of Commons.
Foreign Affairs Minister John Baird said it's a symbolic effort, but sends a disapproving message to the government in Ukraine.
Tougher measures could come if the Ukrainian government fails to respond to popular demands for freedom and democracy, he added.
"We'll see just how things evolve," Baird said. "If further action is necessary, we are prepared to take that action."
There have been some encouraging moves in Ukraine, including the resignation of the prime minister and the repeal of anti-protest laws that sparked violent clashes between protesters and police.
But President Viktor Yanukovych remains in power. The protesters have demanded that he quit and that new elections be held.
Baird said the latest moves aren't enough.
"Even though we're encouraged by recent developments in the last 24 hours, the Ukrainian government must accede to the fundamental demands of its people particularly with respect to accountability and the principles of democracy," Baird said.
Alexander said Canada condemns the killing of protesters, describing the actions of "Ukraine's ruling elite" as "utterly deplorable."
Baird warned against a return to past tyranny. "The backward slide to Soviet-style repression and intimidation is not acceptable."
The steps taken by the government Tuesday did little to mollify Liberal critic John McCallum, who described it as "the absolute minimum and largely meaningless."
New Democrats echoed that disdain, urging the government to implement targeted, personal sanctions aimed directly at the leadership of the Yanukovych regime.
Foreign affairs critic Paul Dewar called for expedited visas for those fleeing the country and urged Prime Minister Stephen Harper to get personally involved by placing a call to the Ukrainian president.
"We should be sending a clear signal that we are serious and that there are consequences for the kind of bloodshed we've seen," Dewar said.
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