A source close to the case confirmed after an autopsy was carried out on her body on Friday afternoon that the 33-year-old died from natural causes.
Speaking after his quarter-final victory over Switzerland's Stanislas Wawrinka at the Shanghai Masters, Nadal said it was "very bad news for the world of sport in general, for Spanish sport especially".
"It's very difficult to say things on day like today," he said. "Stay positive. All the best for her family. Very difficult to find a word because is a very sad, sad day for all of us.
De Villota was in the Andalusian city to take part in a conference organised by the "What Really Matters" foundation promoting human values and was due to launch her book titled "Life is a gift" in Madrid on Monday.
The daughter of former Formula 1 driver Emilio De Villota, she was the first Spanish female to enter the sport when she joined the Marussia team in 2012 as a test driver.