Marca sports newspaper said de Villota's family, led by former F1 driver Emilio de Villota, confirmed the death but did not yet know the cause.
"Dear friends, Maria is gone," the Spanish-language statement read.
Spanish F1 driver Fernando Alonso said after Friday practice in Japan: "I just took my helmet off and (manager) Luis (Garcia Abad) told me.
"I can only pray for her and all her family," Alonso is quoted by El Pais newspaper.
De Villota sustained serious head and facial injuries in July last year when the Marussia she was testing at Duxford, UK, inexplicably drove into the loading ramp of a truck.