Previews for the limited engagement are to begin at the American Airlines Theatre on Feb. 16, with an official opening set for March 16.
Ruffalo is taking over the role of Victor Franz from John Turturro, who left the production due to his filming schedule.
Ruffalo was last seen on Broadway in the 2006 revival of Awake and Sing. His many film credits include Marvel's The Avengers, Begin Again and You Can Count on Me.
"When the Great Depression cost his family their fortune, Victor Franz gave up his dream of an education to support his father," a synopsis said. "Three decades later, Victor has returned to his childhood home to sell the remainder of his parents' estate. His wife, his estranged brother, and the wily furniture dealer hired to appraise their possessions all arrive with their own agendas, forcing Victor to confront a question, long-stifled, about the value of his sacrifice. One of the most personal plays by the consummate voice of the American everyman, Arthur Miller's The Price is a riveting story about the struggle to make peace with the past and create hope for the future."