Ingólfur Vilhjálmsson studied clarinet in Amsterdam with Herman Braune and Harmen de Boer as well as bass clarinet with Harry Sparnaay and Eric van Deuren. He plays all the clarinets and has a great preference for the bass clarinet which he performs regularly, also as a solo instrument. He received a scholarship as a member of the Ensemble Modern Academy in 2006-2007.
He is a member of Ensemble Adapter in Berlin. Ingólfur has worked with many composers of his generation and given concerts in Germany, The Netherlands, Finland and Iceland, including festivals like MärzMusik (Berlin), Ultraschall (Berlin), Dark Music Days (Reykjavik), Frum- (Reykjavík) and Darmstädter Ferienkurse für Neue Musik (Germany). Ingólfur has worked with known composers such as Hosokawa and with Lachenmann on his avant garde landmark piece Dal niente. His playing has been recorded by the WDR, The Icelandic Radio, SWR and the Hessische Rundfunk.
Ingólfur recorded the CD "Dualism" with percussionist Tobias Guttmann on the ITM label in 2008.
As a soloist Ingólfur toured the UK in 2015 and recorded his second CD in 2017 with solo bass clarinet and contrabass clarinet music. The new CD includes music by Franco Donatoni, Alistair Zaldua, Jesper Pedersen, Jakob Diehl and Thrainn Hjalmarsson. Vilhjálmsson's repertoire spans from the classics of the modern repertoire like Dialogue de l'ombre double by Boulez, Clair by Donatoni to the new solo works he regularly commissions and performs. Ingólfur has recorded all the solo clarinet works of Franco Donatoni.
In the classical field Ingólfur works with renowned violinist Judith Ingolfsson and pianist Vladimir Stoupel and performes often with them in Germany and France.