The incident happened after Baird left a meeting with his Palestinian counterpart, Riyad al-Malki at the start of an official trip to the region.
Ahead of the visit, several youth movements, including one affiliated with the Fatah movement of Palestinian president Mahmud Abbas, had called for demonstrations against the visit by Baird.
Canada is one of Israel's staunchest allies and was one of the few countries that opposed a successful Palestinian bid to win upgraded status at the United Nations in 2012.
Last year, during a deadly 50-day summer war in Gaza in which nearly 2,200 Palestinians were killed, drawing sharp international condemnation, Canada said Israel had the right to defend itself and blamed the bloodshed on Hamas.
And in 2013, Baird angered the Palestinians by meeting an Israeli official in occupied east Jerusalem. Such a move is routinely avoided by visiting diplomats because it could be seen as legitimising Israel's annexation of the eastern sector of the city, following the 1967 Six Day War, which was not recognised internationally.
During his meeting with Malki, Baird warned the Palestinians against pursuing any diplomatic agenda which could prejudice the outcome of any future talks with Israel, in a thinly-veiled illusion to Palestinian attempts to seek international recognition following the collapse of the peace process.
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Part of that diplomatic strategy includes a move to join the International Criminal Court (ICC) where they are looking to sue Israel for alleged war crimes in a move strongly opposed by Washington.
"I asked that the minister strongly reconsider the consequences of moving forward with any action that may be counterproductive to a negotiated solution with the state of Israel," Baird said in a statement issued by the Canadian foreign ministry.
He said the two had "constructive talks" which included "candid and frank exchanges on areas where we differ in opinion."
After leaving Ramallah, Baird headed to Jerusalem for talks with his Israeli counterpart Avigdor Lieberman and President Reuven Rivlin.
Palestinian negotiator Saeb Erakat, who did not meet with Baird, issued a statement expressing anger over Canada's unwavering support for Israel and its attempts to block all Palestinian diplomatic initiatives aimed at securing statehood.
"We regret the Canadian government’s decision to stand on the wrong side of history by blindly supporting the Israeli occupation and its apartheid policies," he said.
"Canadian Foreign Minister John Baird has contributed to Israeli violations of Palestinian inalienable rights, including our right to self-determination, by systematically lobbying against all Palestinian diplomatic initiatives," he said.
"The Palestinian people as well as the rest of the Arab and Muslim countries deserve an apology from the Canadian government for years of systematic attempts at blocking the right of the Palestinian people to a state of their own."