Andic reportedly fell down a 150-metre ravine while hiking in an area of the Montserrat mountains known for its deep caves.
Police were called at around 13:00 local time (12:00 GMT), and a helicopter and specialised mountain unit was sent to the scene, El Pais reported.
Mango CEO Toni Ruiz said in a statement: “His departure leaves a huge void but all of us are, in some way, his legacy and the testimony of his achievements.
“It is up to us, and this is the best tribute we can make to Isak and which we will fulfil, to ensure that Mango continues to be the project that Isak aspired to and of which he would feel proud.”
Spanish Prime Minister Pedro Sanchez confirmed Andic died in an accident at the Salnitre de Collbató caves.
“All my love and recognition for your great work and business vision, which has turned this Spanish firm into a world leader in fashion,” Sanchez said.