Canadian Foreign Affairs alerted its citizens in Bangladesh that the Dhaka facility would be shut down and provided a telephone number for assistance.
Canada earlier had not opted to follow the lead of the Unites States, Britain and Germany in closing several embassies and consulates in the Middle East and North Africa.
The Toronto Star said Bangladesh, a neighbor of India, was not immune from the presence of al-Qaida and the Canadian Embassy was located close to the U.S. mission in Dhaka.
Meanwhile, U.S. military forces in the Middle East region were on alert and 22 diplomatic missions were closed Sunday due to terrorism concerns, officials said.
A recent surge of intelligence has pointed to a possible plot by al-Qaida to strike somewhere in the Middle East or North Africa, and the Obama administration decided to close various embassies and consulates Sunday as a precaution.
"The president instructed his national security team to take all appropriate steps to protect the American people in light of a potential threat occurring in or emanating from the Arabian Peninsula," the White House said in a written statement.
Obama met Saturday with high-ranking national security officials Saturday and the statement added the president "received frequent briefings over the last week on all aspects of the potential threat and our preparedness measures."
The U.S. preparedness measures also included raising the alert status of various military units in southern Europe as well as in the Middle East and North Africa.
Sources told CNN a pair of Navy amphibious ships had moved closer to the volatile African nation of Yemen, which is considered a likely potential target of the reported al-Qaida operation. U.S. Marines in Spain and Italy were also ready to immediately respond to trouble.
Sunday was considered to be particularly worrisome because it marks the end of Ramadan. Sunday is considered the "Night of Power" by Muslims and one of the holiest days in Islam.
"It all leads us to believe something could happen in the near future," a senior U.S. intelligence official told CNN.