Martin is biracial: his father, Russell Martin Sr., is Black Canadian, while his mother, Suzanne Jeanson, is Franco-Manitoban. His full name is Russell Nathan Coltrane Jeanson Martin Jr. He was named Russell for his father, Nathan for a great-grandfather, Jeanson after his mother's family, and Coltrane to pay homage to musician John Coltrane, whom his father admired. Martin's parents separated when Martin was two years old. His father used to play saxophone in Montreal metro stations to help pay for his son's baseball training. Martin Sr. played "O Canada" on his saxophone before a 2015 spring training game.