The incident has ratcheted up tensions between the two countries, and sparked an emergency meeting of the political representatives of NATO, of which Turkey is a member.
The blast appeared to come from forces of the regime of Syrian President Bashar Assad, which is fighting rebels backed by Turkey.
"Canada strongly condemns, in no uncertain terms, this attack by the Assad regime across Turkey's border, which killed five people including a six-year-old child," Baird told a brief news conference in the foyer of the House of Commons Wednesday.
"All countries must bring pressure to bear on Syria for Assad to go."
Turkish media say a Syrian missile hit a house in the Turkish village of Akcakale, killing five civilians, including children, and wounding a dozen others.
"Canada calls for calm and for the Assad regime to stop drawing the region into a self-inflicted conflict and war on the Syrian people," said Baird.
"The Syrian people deserve better than this illegitimate and murderous regime."
NATO's National Atlantic Council issued a statement Wednesday that Baird said Canada backs.
"The alliance continues to stand by Turkey and demands the immediate cessation of such aggressive acts against an ally," NATO said, as it urged the Assad regime to "put an end to flagrant violations of international law."
Baird echoed the calls of allies for cooler heads to prevail. He dismissed any suggestion of military intervention.
"In the first few hours of this I think that would be incredibly premature," Baird said.
"We obviously recognize that every country has a right to defend itself. I think we do have to appeal for calm, to not let this situation escalate out of control."
The New Democrats also condemned the Syrian attack and expressed concern about rising tensions in the region.
"We call on the Syrian government to immediately cease all violence against its neighbouring countries and against its own civilians," NDP Foreign Affairs critic Paul Dewar said in a statement.
"This is an important moment for international leadership to de-escalate tensions. The Security Council of the United Nations should be seized with finding a resolution to this crisis. Canada must be engaged in these discussions and in discussions at NATO."
Wednesday's fatal rocket attack was not the first incident between Turkey and Syria, since the uprising against the Assad regime began last year.
The most recent incident occurred in June, when Syria shot down a Turkish jet, killing two pilots.
Baird said Canada has imposed tough sanctions on Syria and will continue to work with international partners to isolate the Assad regime.
Turkish Prime Minister Recep Tayyip Erdogan issued a strongly worded statement that said: "Turkey, acting within the rules of engagement and international laws, will never leave unreciprocated such provocations by the Syrian regime against our national security."
Turkey's Anadolu agency reported that the government is considering a bill that could pave the way for unilateral military action against Syria. The bill is similar to a law that allows Turkey's forces to pursue Kurdish militants to their bases in northern Iraq.
Turkey wants to avoid going into Syria on its own. It has been pushing for international intervention in the form of a safe zone, which would likely entail foreign security forces on the ground and a partial no-fly zone.
However, the allies fear military intervention in Syria could ignite a wider conflict, and few observers expect robust action from the United States, which Turkey views as vital to any operation in Syria, ahead of the American presidential election in November.
Turkey, which has moved military reinforcements to the border in recent months, has more than 90,000 Syrian refugees in camps along its border, and also hosts Syrian opposition groups.
United Nations Secretary General Ban Ki-moon called on Syria to respect the territorial integrity of its neighbour.
Baird has criticized the UN Security Council for its inaction on Syria.
U.S. Secretary of State Hillary Clinton expressed outrage at the border shooting.
"It's a very, very dangerous situation," she said. "And all responsible nations need to band together to persuade the Assad regime to have a cease-fire, quit assaulting their own people and begin the process of a political transition."
— with files from the Associated Press
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