He won an Oscar in 2012 for the film Beginners and was also nominated for The Last Station in 2010 and All the Money in the World in 2018.
In the latter film he replaced Kevin Spacey, whose complete performance as billionaire J Paul Getty was excised.
His many other films included The Man Who Would Be King and Knives Out.
According to reports, Plummer passed away peacefully at his home in Connecticut with his wife Elaine Taylor at his side.
Lou Pitt, his long-time friend and manager of 46 years, remembered him as "an extraordinary man who deeply loved and respected his profession".
"He was a national treasure who deeply relished his Canadian roots," he continued. "Through his art and humanity, he touched all of our hearts and his legendary life will endure for all generations to come.
"He will forever be with us."