Suhonen joined the youth academy of Hamburger SV as a 16-year-old in 2017, moving from the Finnish club KäPa.
Suhonen made his professional debut with the club's first team in a 2–1 German Cup win over Eintracht Braunschweig on 8 August 2021.
His breakthrough was delayed due to multiple injuries. In July 2020, while playing with the HSV II reserve team, Suhonen suffered a knee injury that haunted him ever since in his Bundesliga career.
"Anssi has developed in his time with us from a young junior player to an established professional. On his way, unfortunately, he had to fight with injuries again and again and couldn't exploit his potential over a longer period of time. After these setbacks, he always fought back impressively. Anssi is a player who always gives everything and leaves his heart on the field", says HSV sport director Claus Costa to the HSV website.
OB sports director Troels Bech is delighted with the signing:
"With the arrival of Anssi Suhonen, we are strengthening our options in midfield. Anssi fits into OB's playing style with his pressing intensity, willingness to run, and good passing", says Troels Bech to the club's website.