Museum chairman Ian McDougall says the landlord, Parc Downsview Park, was in the process of changing the locks on Tuesday afternoon.
McDougall says the museum was behind on its rent by about $120,000, but had begun generating more revenue and was in a position to begin making payments.
McDougall says the landlord didn't accept partial payment and ordered all back rent to be paid immediately or the museum would be closed.
Parc Downsview Park, a Crown Corporation that reports to Public Works and Government Services Minister Rona Ambrose, could not be reached for comment.
McDougall says he doesn't know what will happen to the museum's displays, which include a full-size replica of the Avro Arrow and photos and artifacts documenting the history of de Havilland Canada.
"We have the only full-scale replica of the Avro Arrow, which took about 10 years for people to build," McDougall said. "The museum space is the original factory from which Tiger Moths, Beavers, Otters, Twin Otters and Mosquito bombers emerged."
McDougall said he finds it surprising that such an important part of Canada's aviation and industrial history would be taken and converted into hockey rinks.
"No one's told me that there's a shortage of hockey rinks in Canada — that's new to me," he said.
Coun. Maria Augimeri, who represents the Downsview area on Toronto city council, said Tuesday that she was shocked by the closure and appealed to Ottawa to help the museum.
"It shows that the federal government is so fixated on the bottom line it's even willing to throw the Avro Arrow to the curb for collection," Augimeri said.