Jones is the son of Brad Jones, an eighth-round pick (No. 156) in the 1984 NHL Draft who played 148 NHL games for the Winnipeg Jets, Los Angeles Kings and Philadelphia Flyers from 1986 to 1992. A native of Rochester, Michigan, Max Jones played in the junior Honeybaked Hockey program before joining the USA Hockey National Team Development Program for the 2014-15 season.

Jones was selected by London in the first round (No. 18) of the 2014 Ontario Hockey League Priority Selection Draft and joined the Knights for the 2015-16 season. He had 52 points (28 goals, 24 assists) in 63 regular-season games and helped London win the Memorial Cup by getting an assist in a 3-2 victory against Rouyn-Noranda in the final.

Chosen by the Anaheim Ducks with the No. 24 pick in the 2016 NHL Draft, Jones was assigned to San Diego of the American Hockey League for the remainder of the 2017 Calder Cup Playoffs after London was eliminated from the OHL playoffs. He was traded by London to Kingston on Jan. 7, 2018 and helped the Frontenacs reach the Eastern Conference final.

Jones began 2018-19 in the AHL, was called up by the Ducks on Jan. 16, 2019 and played the final 30 games of the regular season. He earned a full-time role in Anaheim in 2019-20.

After six seasons with the Ducks, Jones signed a two-year, $2 million contract with the Boston Bruins on July 1, 2024. He played seven games for the Bruins that season before he was traded to the Edmonton Oilers in a three-team deal involving the New Jersey Devils on March 4, 2025.