The couple, who lived in the southeastern city of Alicante, were keeping the clothes in boxes stacked in their bedroom to sell them off again, according to the Diario Informacion.
Their eldest, 18-year-old daughter made the grim discovery on Saturday when she woke up, found that the flat was quiet, went into her parents' room and found all the boxes collapsed on the bed, it said.
She couldn't see her parents or her sister under what was estimated to be one to two tonnes of clothes, and called the police, it added.
Officers managed to locate and pull out the younger daughter, but were unable to revive her.
Firefighters were later called in for help to extract the parents from under the mountain of clothes, the daily said, adding it was unclear why the stack of boxes collapsed.
Police and firefighters were not immediately available for comment.