Muñoz is of Greek descent on his mother's side.[4]
His nickname is "el tibio", which means "lukewarm" in Spanish, a nickname which has multiple possible explanations. According to some sources, it was coined because he had the habit of refusing to swim in an unheated pool.[5] However, other sources, including the International Swimming Hall of Fame, have stated that it was because his mother was from the town of Río Frío (meaning Cold River) and his father was from the town of Aguascalientes (meaning Hot Waters).[6]