Baird, who met Wednesday with Syrian and Syrian-Canadian human rights activists, said Canada is working with its allies to ensure the weapons don't fall into the wrong hands as the conflict reaches a climax.
"We're concerned about two things: them being used against the Syrian people, and two, we're concerned about their security both before and after the regime would fall," Baird said.
The wrong hands could belong to Islamic extremists, Baird suggested, including al-Qaida cells that have reportedly infiltrated the clashes between the regime of Bashar al-Assad and rebel forces, or other terrorist organizations.
The Israeli government has expressed concern that Lebanon's Hezbollah might try to secure some of the weapons of mass destruction. There has been a run on gas masks inside of Israel.
The Conservative government remains resistant to supporting military action in Syria, despite Baird's view that "there's no room for Assad in any effort to negotiate a solution."
"Just because a military solution worked in one part of the world, doesn't mean it will work in another," he said.
"I think there's a consensus among Canada and its allies and others that we need to continue to push hard on the diplomatic side. Obviously we share the frustration that we haven't met with success, but we're not simply going to throw in the towel."
Members of the Syrian National Council and the Syrian Canadian Council, as well as a Roman Catholic priest exiled from Syria after 30 years of interfaith work, pressed Baird during their meeting for more humanitarian assistance in the country.
Canada has currently earmarked $8.5 million for helping those caught up in the conflict, but the activists are asking for Baird to come up with $25 million.
"Hospitals in Syria have become detention centres, so a project that would finance mobile hospitals is a priority for us," said Faisal Al Azem.
Baird said Canada "can and does want to do more."
Father Paolo Dall'Oglio, an Italian-born Jesuit priest who ministered from a desert monastery outside of Damascus until he was exiled in June, suggested Canada could be using its expertise with Russia to help the cause.
Both Russia and China have blocked United Nations Security Council efforts to impose sanctions on Syria. Russian officials have pointed to evidence of al-Qaida cells in Syria as a rationale for not moving to oust Assad.
"There is plenty of work with Russia that is ongoing every day to fix issues related geographically with the (Arctic), so there are channels," said Dall'Oglio.
"There is knowledge, there is know-how about the relationship with Russia and geo-strategic exigencies. We ask Canada to use this know-how to start again a round of diplomacy activity."
Dall'Oglio added that Canada could help with peacekeeping or "peace promoting" efforts once the Assad regime falls and civil society must be bolstered.
Baird said earlier that he's had discussions with his Russian counterpart and the ambassador.
"I think Canada's voice has been very strong: Russia's actions, not inactions, are enabling this regime to soldier on."
Baird also noted Canada's alarm at the use of helicopters and fixed-wing aircraft by Syrian troops.
On Wednesday, the regime beefed up its forces heading towards the commercial capital of Aleppo. Rebels have already moved into a large part of the city.