He was born in Stranda, Norway, and educated at the Trondheim Conservatory. It was during his time at the conservatory that a friend gave him a tape recording of the shakuhachi flute. Henriksen was hooked. "I let the music 'ring' and develop in my head," he said. "I was astonished by the sound of this flute." His interest in minimalist Japanese music had a profound effect on his trumpet playing and his music career.

Henriksen collaborated with numerous musicians on avant-garde, minimalist, and Eastern-influenced music, working with artists such as Anders Jormin, Edward Vesala, and the Source before striking out on his own with 2001's Sakuteiki. He is also trumpeter in the improvisational jazz groups Supersilent and Food, with Thomas Strønen, Iain Ballamy, and Mats Eilertsen; the latter recorded their debut, Veggie, in 2002.

Several albums followed over the years, including 2004's critically acclaimed Chiaroscuro, 2007's Strjon, and his acclaimed ECM debut, Cartography, in 2009. Henriksen's credits also include contributions to the works of other artists such as the Christian Wallumrød Ensemble, Arild Andersen, Jon Balke, Sinikka Langeland Ensemble, and David Sylvian, among others.

In 2012, he recorded Black Swan in duet with drummer Teun Verbruggen, and followed it with the vinyl-only box set Solidification, which collected his first three albums with bonus material, and a new recording entitled Chron. In 2013, he issued the completely solo Places of Worship to wide acclaim. The Solidification box set had sold well, yet fans who purchased the earlier recordings in their initial releases demanded that Chron be issued on its own. Henriksen and Rune Grammofon accommodated them. In February of 2014, they re-released it in a double package with a companion disc of new material and titled it Chron + Cosmic Creation.

Later that fall, he released The Nature of Connections, an album of new material that was closer to contemporary chamber music and North European folk than anything he'd done previously. The compositions were almost exclusively written by his collaborators, who included violinists Nils Økland and Gjermund Larsen, cellist Svante Henryson, double bassist Mats Eilertsen, and drummer Audun Kleive. For the next few years, Henriksen spent his time as a collaborator. He appeared on several recordings including Gjertrud Lunde's Hjemklang (2014), Langeland's The Magical Forest, and Tigran Hamsayan's Atmospheres (both for ECM in 2016). ~ Margaret Reges