Shortly before Mr Trudeau’s tweet, the North American Aerospace Defence Command said it had detected an object flying at high altitude over Canada.
Norad gave no further information, including when the object was first spotted or what it is.
A spokesman, Major Olivier Gallant, said both Canadian and US warplanes operating as part of Norad had been deployed.
On Twitter, Mr Trudeau said: “I ordered the take down of an unidentified object that violated Canadian airspace. @NORADCommand shot down the object over the Yukon. Canadian and US aircraft were scrambled, and a US F-22 successfully fired at the object.”
The object was the third known to have violated North American airspace in the past two weeks.
In a second tweet, Mr Trudeau said: “I spoke with President Biden this afternoon. Canadian Forces will now recover and analyse the wreckage of the object. Thank you to Norad for keeping the watch over North America.”
A suspected Chinese spy balloon spent nearly a week flying through Canadian and US airspace before it was shot down by US warplanes last Sunday.
The US military shot down a second object in Alaskan airspace on Friday, though authorities have not provided details on what it was.
According to US Northern Command, recovery operations continued on Saturday both near Deadhorse, Alaska, and off South Carolina.
In a statement, the Northern Command said there were no new details on what the object was that a US fighter jet shot down over Alaska.
It said the Alaska Command and the Alaska National Guard, along with the FBI and local law enforcement, were conducting search and recovery.
“Arctic weather conditions, including wind chill, snow, and limited daylight, are a factor in this operation, and personnel will adjust recovery operations to maintain safety,” the statement said.
“Recovery activities are occurring on sea ice.”
It added that the Navy continued survey and recovery activities on the ocean floor off South Carolina, and the Coast Guard was providing security.
Additional debris was pulled out on Friday, and additional operations will continue as weather permits, the statement said.