The 33-year-old was found dead in a hotel room in Seville on Friday morning.
"The cause of death was natural. We cannot say much more at this stage out of respect to the family," the source said.
De Villota was in the Andalusian city to take part in a conference organized 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.
However, just four months later De Villota suffered severe injuries, including the loss of her right eye in a crash while testing at Duxford Airfield in Cambridgeshire.
"I hope that, without having to go through an accident like mine, you can feel the joy of being alive and enjoy life," she wrote in the introduction to the book to explain the motivation behind it.
"Maria has left us. She had to go to heaven like all the angels. I give thanks to God for the extra year and a half he left her with us," read a message from her family posted on De Villota's Facebook page.
"It is with great sadness that we learned a short time ago of the news that Maria de Villota has passed away," the Marussia team said in a statement.
"Our thoughts and prayers are with Maria's family and friends at this very difficult time."
The news has shocked the world of motorsport with tributes to a female pioneer in the sport pouring in.
De Villota had hoped to become just the third woman in history to take part in a Formula One race and Sauber team principal Monisha Kaltenborn, who became the first female team principal in the sport in 2012, hopes she has left a legacy for future female drivers to follow.
"If anybody represented strength and optimism, it was María," she said.
"Her sudden death is a big loss to the motorsport world as she was an important ambassador for relaying important messages to the youth, and particularly girls that aspire to a career in motorsport. Maria was an example of someone who never gave up, she always had a smile on her face and we will dearly miss her."
"She gave young girls strength. Undergoing what she did and to still come out there and still be so convinced.
"Even if she maybe couldn't drive in Formula One the way she dreamt (after the crash), she didn't give up her passion. Hopefully she has made a difference. Now it's up to us to transfer that message further."
Two-time Formula One champion Fernando Alonso said he was in shock after finding out the news ahead of the Japanese Grand Prix at Suzuka this weekend.
"It's hard to talk about Maria de Villota right now, as I had only just taken my helmet off, when I was told about her death and at the moment, I still can't believe it and need a while to stop and think about it," he said.
"Of course, it's very sad news for the world of motorsport as Maria was loved by everyone. Now, all we can do is pray for her and for her family."
The President of the Spanish Automobile Federation, Carlos Gracia also added his condolences.
"I have just found out. It is a very hard to take. There is no explanation for what has happened," he told Spanish National Radio.
"She was a great person and an example for everyone."