Murray was born and raised in Kitchener, Ontario , the son of Sylvia and Roger Murray, who was born in Jamaica and moved to Canada at age nine.    He also has a younger brother, Lamar. His father grew up running track and field and playing basketball; as a youth, his father played against Kitchener native Lennox Lewis before Lewis began his professional boxing career. 
When Murray was three years old, he could play basketball "for hours" and played in a league for ten-year-olds when he was six.   By the age of 12 or 13, he began playing pick-up games against top high school and college players. His father put him through many basketball drills and kung fu exercises, including meditation .  
High school career
Murray attended Grand River Collegiate Institute in Kitchener, later transferring to Orangeville Prep in Orangeville, Ontario , where his father served as an assistant coach.  He and fellow prospect Thon Maker formed a duo that would help Orangeville Prep defeat many American schools. 
On June 24, 2015, Murray committed to Kentucky to play for coach John Calipari .    Murray is the only Kentucky player to have scored over 30 points in more than one game during a freshman season. He is currently tied with Terrence Jones for most points in a game by a UK freshman (35). He was featured on the Midseason Top 25 list for the John R. Wooden Award on January 13, 2016.  He was also named to the 35-man midseason watchlist for the Naismith Trophy on February 11. 
Murray represented Canada at the 2013 FIBA Americas Under-16 Championship in Uruguay , and averaged 17 points, 6 rebounds and 2.4 steals per game in leading the team to a bronze medal.  He played for the Canadian national team at the 2015 Pan American Games , helping the team win a silver medal.  His final averages for the tournament were 16.0 points, 3.2 rebounds and 2.4 assists per game, while shooting 45.9% from the field.