[1] After early years with the Tier 1 Ohio AAA Blue Jackets, Kuraly played four games in the U.S. National Development Team Program before joining the Indiana Ice of the United States Hockey League (USHL).

After his first full rookie season with the Ice, Kuraly was selected by the San Jose Sharks in the fifth round, 133rd overall, of the 2011 NHL Entry Draft.

He helped guide the RedHawks to the 2013 CCHA Men's Ice Hockey Tournament, where he scored the game-winning goal to defeat Michigan State University in the quarterfinals.

[11] Kuraly scored his first two career goals, including the double overtime winner, in a 3–2 win in Game 5 of the 2017 Eastern Conference Quarterfinals against the Ottawa Senators.

[12] Following the 2020–21 season, his fifth with the Boston Bruins, Kuraly left the organization as a free agent and was signed to a four-year, 10 million contract with hometown club, the Columbus Blue Jackets, on July 28, 2021.