The Canadian actor died at home on Friday in Connecticut, in the US, according to his manager.
Dame Julie, 85 – who starred opposite Plummer in the 1965 hit, labelled him a “consummate actor” and a “cherished friend”.
In a statement to the PA news agency, she added: “I treasure the memories of our work together and all the humour and fun we shared through the years.
“My heart and condolences go out to his lovely wife Elaine and his daughter Amanda.”
Plummer enjoyed a varied career across film, television and theatre and in 2012 became the oldest actor to win an Oscar.
He was handed the best supporting actor gong for his part in Beginners.