He played one season of college basketball for the Kentucky Wildcats before being selected by the Nuggets as the seventh overall pick in the 2016 NBA draft.

[6] He and fellow prospect Thon Maker formed a duo that helped Orangeville Prep defeat many American schools.

[2] At the 2013 Jordan Brand Classic International Game, Murray was named MVP, becoming the second Canadian to win the award after Duane Notice.

[8][9] Murray was named MVP of the 2015 BioSteel All-Canadian Basketball Game, which includes the top high school players in Canada.

[16] Murray's 20.0 points per game are the most by any freshman in Kentucky's program history and the most for any player in John Calipari's tenure as head coach.

[17] He led the Wildcats, who had seven future NBA players on the roster, to a #1 ranking early in the season and the SEC title prior to being upset by 5-seed Indiana in the second round of March Madness.

[29] On January 22, 2018, he scored a career-high 38 points, including a three-point play in the final minute, as the Nuggets beat the Portland Trail Blazers 104–101.

[38] On February 6, after missing six games with a sprained left ankle, Murray had 19 points and 11 assists in a 135–130 loss to the Brooklyn Nets.

[41] On the first day of free agency period, Murray signed a contract extension of a 5-year, $170 million maximum deal with the Nuggets.

[43] Three days later, during a 105–95 victory over the Houston Rockets, Murray recorded a career-high 6 steals, along with scoring 10 points and adding 9 assists.

[44] On December 23, Murray scored 28 points and would knock down a game-winning step-back jumper against the Phoenix Suns with 2.5 seconds remaining in overtime to secure a 113–111 road victory.

[49] On March 4, Murray hit yet another game-winner, making an off-balance jumper with 4.5 seconds remaining in regulation to seal a 114–112 victory over the Hornets while capping off an 18-point, 6-assist performance.

[54][55] Following Game 6, Murray became emotional during the postgame interview with TNT’s Jared Greenberg, addressing racial injustice, as well as honoring George Floyd and Breonna Taylor, as each of their pictures were on his shoes.

[56] On September 15, in Game 7 against the Los Angeles Clippers, Murray scored 40 points while hitting six three-pointers, leading the Nuggets to a series-clinching 104–89 win to advance to the Western Conference Finals for the first time since 2009.

[73] In Game 1 of the Western Conference Semifinals, Murray recorded 34 points, 5 rebounds and 9 assists in a 125–107 win over the Phoenix Suns.

[74] In Game 2 of the Western Conference Finals, Murray scored 23 of his 37 points in the fourth quarter, along with 10 rebounds, 5 assists and 4 steals, propelling the Nuggets to a 108–103 come-from-behind win over the Los Angeles Lakers for a 2–0 lead in the series.

[75] In Game 3 of the Western Conference Finals, Murray scored 30 of his 37 points in the first half, along with seven rebounds and six assists in a 119–108 win, helping the Nuggets take a commanding 3–0 series lead.

[80] In Game 5, Murray put up 14 points, eight rebounds, and eight assists in a 94–89 win over the Heat to help lead the Nuggets to their first NBA championship in franchise history.

[81][82] On April 22, 2024, in Game 2 of the first round of the playoffs against the Los Angeles Lakers, Murray put up 20 points along with a buzzer-beating, game-winning fadeaway jump shot over Anthony Davis in a 101–99 victory as the Nuggets took a 2–0 lead.

[85][86] On May 6, 2024, during Game 2 of the Conference Semifinals against the Minnesota Timberwolves, Murray threw a heat pack and towel towards the court while he was on the bench.

[93] 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.

[96] He joined Canada in their preparations for the 2023 FIBA Basketball World Cup, but eventually decided to miss the competition to recover from his championship-winning NBA season.