She was visiting Thailand with her boyfriend, who witnessed the attack.
Spanish Foreign Minister Jose Manuel Albarez said the Spanish consulate in Bangkok was helping the Garcia family.
BBC News has contacted the elephant care center for comment.
Bathing elephants is a popular activity among tourists in Thailand, which is home to more than 4,000 wild animals and the same number in captivity, according to the National Parks Department.
The Koh Yao Center offers elephant care packages that allow tourists to cook and feed the animals, as well as shower and walk them. These packages cost between 1,900 baht ($55; £44) and 2,900 baht.
Animal rights activists have previously criticized elephant bathing, saying it disrupts the animals’ natural grooming behavior and exposes the animals to unnecessary stress and possible injury.
The international charity World Animal Protection has for years called on countries, including Thailand, to stop breeding elephants in captivity.
More than six in 10 elephants used for tourism in Asia live in “grossly inadequate” conditions, a charity has said.
“These intelligent and socially complex animals, capable of complex thought and emotion, suffer profoundly in captivity as their natural social structures cannot be reproduced artificially,” the charity said.
