Brooks was drafted by the Houston Rockets with the 45th pick in the 2017 NBA draft and then was immediately traded to the Memphis Grizzlies. On July 21, 2017, the Grizzlies signed Brooks to his rookie scale contract. On October 18, 2017, during the Grizzlies' season opener, Brooks scored 19 points, the most points scored by a Canadian-born player in an NBA debut.

On April 11, 2018, Brooks scored 36 points along with seven rebounds, one assist, and two steals in a 137–123 loss against the Oklahoma City Thunder. In December 2018, Brooks was thought to be involved in a failed three-way trade between Memphis, the Washington Wizards and the Phoenix Suns; the trade faltered over confusion between Brooks and his similarly named teammate, MarShon Brooks, as the Memphis front office did not intend to trade Dillon while the other teams expected him and not MarShon.

On January 5, 2019, Brooks suffered from a ruptured ligament in his right big toe and underwent a successful surgery to repair it on January 11, 2019. Brooks missed the remainder of the 2018–19 season.

Brooks began the 2019–20 season as the Grizzlies' st…

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Brooks played for the Canadian national team in the 2015 Pan American Games, where the team won the silver medal.

On May 24, 2022, Brooks was one of fourteen players to agree to a three-year commitment to play with the Canadian senior men's national team, aiming to break a decades-long trend of failing to qualify for the Olympic basketball tournament. They achieved this goal at the 2023 FIBA World Cup, and won the bronze medal, Canada's first global tournament medal in basketball since 1936. Brooks played a crucial role, recording a team-best 39 points in their victory over the United States. This was a single-game scoring record for a Canadian player at the World Cup, surpassing Carl Ridd's previous high of 37 at the 1954 edition. Brooks was named Best Defensive Player of the tournament by FIBA.

He was named to Canada's roster for the 2024 Summer Olympics in Paris.

In 2024, Brooks became an angel investor in Panda Hub, a mobile car detailing marketplace operating in North America. His involvement began as a customer in Houston, Texas, where he utilized the service and later decided to invest, citing the company's innovative approach to simplifying car care through technology. Brooks' investment aligns with his interest in ventures that address everyday problems and offer passive income opportunities.