In 1562, he accompanied his fathers and brothers Giovanni and Ferdinando, at the Tuscan coast to embark to Spain, where the eldest son Francesco lived. But his mother Eleanor, and the children contracted malaria and all except Ferdinando, died in a few weeks.
Many of sudden deaths in the family of the Duke immediately aroused the suspicions of the family, who also attended the Council of Trent. Several sources confirm, however, that during the period there was a violent flu epidemic.
Centuries after his death, a myth arose saying that Garzia, had murdered his brother, Giovanni, following a dispute in 1562. In turn, his father Cosimo, furious, killed Garzia with his own sword. However, modern exhumations showed no signs of violence on the bodies and found to have died together of malaria in 1562.