Isak Andic, a 71-year-old billionaire, died on Saturday, Mango’s chief executive Tony Ruiz said in a statement.
Spanish media reported that the businessman slipped and fell from a cliff while hiking with his family in mountains near Barcelona.
Mr Andic was born in Istanbul, but moved to Catalonia in the 1960s.
He founded Mango in 1984. The brand’s first UK store opened in 1999 and there are now more than 60 branches across the country.
In a statement, Mr Ruiz said: “Isak has been an example for all of us.
“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.”