His son, Ian, confirmed the death noting that Finkel had been suffering from heart problems for several months, according to The Hollywood Reporter.
Finkel began his career with Yiddish theatre shows at the age of nine.
While he was popular in his niche stage community, the actor entered the industry in 1964 with the national production of "Fiddler on the Roof," in which he played Mordcha.
He began touring in "Fiddler on the Roof", playing various roles until he eventually starred as Tevye. In 1988, Finkel won an Obie Award for his role in the revival of "Cafe Crown".
The actor is survived by his two sons, Ian and Elliot.