Azurmendi is a Basque surname. Notable people with the surname include:
Clara Azurmendi (born 1998), Spanish badminton player Eneko Azurmendi (born 1977), Basque chef Joxe Azurmendi (1941–2025), Basque writer, philosopher, essayist, and poet Mikel Azurmendi (1942–2021), Spanish anthropologist Nora Azurmendi (born 1995), Spanish handballer