Prior to the 2004–05 NHL lockout, Kasperi Kapanen's father, Sami Kapanen, was part of a group that purchased the latter's junior team in Finland, KalPa. Having owned the team since, it was no surprise when Kasperi Kapanen made his bantam debut with KalPa's under-16 affiliate in the Jr. C SM-Sarja. Kasperi Kapanen led the team in goals and was second in points, though failed to help them win their playoff qualifier. The following year, as a 15-year-old, Kasperi spent only eight games on the under-16 squad (scoring 16 points in the process) before graduating to the under-18 team playing in the Jr. B SM-Sarja. Kapanen continued his torrid scoring with 24 points in 25 games, finishing second in both goals (13) and points. His third season in Finland's junior system saw more of the same as he swiftly advanced to the under-20 team playing in the Jr. A SM-Liiga and recorded 29 points in 36 games, again leading the team in goals (14) and finishing fourth in points. During the 2012–13 season, he also spent 13 games with the senior KalPa team in the SM-Liiga, Finland's top professional league, playing alongside his father. At the end of the year, Kapanen was selected to play for the Finland under-18 national team at the 2013 IIHF World U18 Championships. Kapanen led Finland in goals and was second in points as he helped the team to a bronze medal finish.