Doohan started last season in a race seat alongside Frenchman Pierre Gasly but lasted only six races before he was replaced by Argentine Franco Colapinto.
The 22-year-old son of five-time motorcycling world champion Mick had remained contracted as a reserve driver for the team.
"BWT Alpine Formula One team confirms it has reached a mutual agreement with Jack Doohan to not continue his driving services with the team for the 2026 ... world championship season and allow him to pursue other career opportunities," the team said in a statement.
"The team would like to thank Jack for his commitment and professionalism to the team for the past four years, both on and off the track, and wishes him all the best for the future."
Colapinto, 22, failed to score a point for Alpine in 18 races last season -- the only driver on the grid apart from Doohan to draw a blank -- but has been confirmed for 2026 alongside Gasly.