Canada will continue to vigilantly monitor developments in Ukraine as the world spotlight shifts to Russia this week, Baird told a news conference Monday.
"The Olympics are an exciting time for the athletes, for the world and for the Olympic spirit, we will very much be keeping an eye on the situation throughout Ukraine," he said.
"We will not be taking our eye off Ukraine for one moment during the Sochi Games."
Baird also registered Canada's outrage at the barbaric kidnapping of an opposition activist who was reportedly crucified by his Ukrainian captors.
"The abduction and abuse of pro-democracy activists is a cruel and crude attempt to deter peaceful protest through fear," he said in a statement. "We call for an independent investigation into this case and all other crimes against protesters."
The Harper government has barred Ukrainian officials from entering Canada because it says the government is suppressing dissent.
For two months now, Ukraine has been rocked by raucous anti-government protests, some of which have turned violent.
The dissent erupted after the government bowed to Russian pressure and abandoned an economic co-operation agreement with Europe.
Baird reiterated the government's position that Ukraine faces a prosperous economic future if it embraces Europe, instead of bowing to its old Soviet Union master.
"Obviously, Ukraine matters to Canada. We want to see peace, prosperity and freedom for the people of Ukraine. We think the European Association agreement, and the government's previous commitment to support that, was the best path forward."
Baird repeated his warning to Canadians attending the Olympics to exercise caution. The threat of terror attacks by Islamic militants from the nearby North Caucasus continues to hang over the Games, which get underway Thursday.
A massive military buildup is underway in Russia to provide security, including two American warships that have been deployed to the Black Sea, as well as tens of thousands of police and military forces, backed by warships and aerial support.
"While we're tremendously concerned about security, we've obviously got to remain focused that this is about the athletes and about the Games," said Baird.
Canada is consulting with its allies on possible next steps towards the Ukraine government, he added.
Canadians of Ukrainian descent have called on Ottawa to target the Ukrainian government with sanctions and asset freezes.
Baird said he is keeping in touch with U.S. Secretary of State John Kerry and his European Union counterpart, Catherine Ashton.
Ashton has said she would return to Kyiv this week, her third visit since the crisis began.
Also on HuffPost