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.