Jonathan Andic, 45, was arrested and questioned by police in Catalonia, then brought to court in handcuffs, where the judge set bail of €1 million ($NZ1.99 million) and required him to hand over his passport.
He left the court after making bail, but cannot leave the region and is required to report to the court once a week.
Isak Andic died after falling more than 100 metres from a cliff while hiking with his son near Barcelona in December 2024. His death was initially treated as an accident.
Judge Raquel Nieto Galvan said in a statement on Tuesday after the court hearing that the case was being investigated as a homicide.
In her writ, she cited evidence pointing to a poor relationship between the two, possible financial motive, prior planning and study of the scene, "autopsy that practically rules out slipping or stumbling", and discrepancies in the suspect's statements, among other factors "that could implicate JA in the death of his father".
The Andic family said in a statement he was innocent.
"There is no legitimate evidence against him, nor will any be found," it said.
In a statement, defence lawyer Cristobal Martell called the homicide theory inconsistent.
"But above all, it is painful. It stigmatises an innocent man. Now the real process begins, and the truth and his innocence will shine through."
A spokesperson for the family said Mango's vice chairman Jonathan Andic would continue to cooperate with authorities and called for the principle of the presumption of innocence to be respected.
Isak Andic, who was born in Istanbul, moved to Catalonia in the northeast of Spain in the 1960s and founded Mango in 1984.
He built it into a global group seen as a rival to Zara, which was started by Galician businessman Amancio Ortega and is now run by his daughter Marta.
At the time of his death, he was non-executive chairman of Mango with a net worth of $US4.5 billion ($NZ7.72 billion) according to Forbes.
Jonathan Andic and his two sisters jointly own 95% of Mango, with 5% owned by Toni Ruiz, its CEO since 2020.
Ruiz became chairman of the board, replacing Isak Andic in January 2025 after his death.
Jonathan Andic, who previously worked in Mango's retail operations, was named vice chairman.
Mango declined to comment on the arrest.
In 2002, the company reached the milestone of having stores on every continent. In 2008, it branched into men's fashion then children's wear in 2013. Mango has around 3000 stores in more than 120 countries.
