Hyvönen started out in the Kärpät junior team, and started playing in the SM-liiga with TPS. He was drafted by the San Jose Sharks as their ninth-round pick in the 1999 NHL Entry Draft. After playing on a number of SM-liiga teams, Hyvönen departed to North America for the 2001–02 season, which he mostly spent with the Sharks' AHL affiliate, the former Cleveland Barons. He was next signed by the Florida Panthers, but the Columbus Blue Jackets signed him from the waivers list before the start of the season. Near the end of the 2002–03 NHL season the Blue Jackets loaned Hyvönen to Färjestads BK in the Swedish Elitserien. He started the 2004–05 NHL lockout season with Färjestad, and later transferred to Ilves in the SM-liiga. In 2005 Hyvönen signed with HC Fribourg-Gottéron in the NLA, but although he led the team in scoring by the start of November, his performance was deemed unsatisfactory and he was sold to Jokerit.