After a stint within the Jokerit junior program, Ylönen returned to the Blues making his professional debut with Espoo United of the Mestis during the 2016–17 season.

Opting to remain in Finland to continue his development, Ylönen joined the top tier Liiga club, the Lahti Pelicans, on a two-year contract in April 2018.

On 1 March 2020, with the Pelicans out of playoff contention, Ylönen opted to sign his first professional contract abroad, agreeing to play the remainder of the season with the Canadiens' American Hockey League (AHL) affiliate, the Laval Rocket.

[7] With the pandemic delaying the beginning of the 2020–21 NHL season, Ylönen was loaned back to the Pelicans to start the 2020–21 campaign, subsequently returning to Montreal with the opening of their respective training camp.

[13] Ylönen scored his first NHL goal on a pass from linemate Drouin on 15 December 2021 in a 5–2 loss to the Pittsburgh Penguins.

His father Juha, a former professional ice hockey centre, won a bronze medal with the Finnish national team at the 1998 Winter Olympics[21] and played a total of six NHL seasons with the Phoenix Coyotes, Tampa Bay Lightning, and Ottawa Senators, being a member of the Coyotes at the time of Jesse's birth.