Maria De Villota, 33, famously lost an eye in a freak accident at Duxford Aerodrome, Cambridgeshire, in July last year.
She was the daughter of former F1 driver Emilio De Villota, and competed in F3, GTs, touring cars and the Superleague Formula before joining up with the Marussia team last year.
It was while testing for Marussia that De Villota lost her right eye.
Despite spending a month in hospital, De Villota rebuilt her life and became part of the FIA's Women In Motorsport commission.
It is thought she was promoting her autobiography at the time of her death, with local media reports stating that she was found in a hotel room in Seville.
A statement on De Villota's Facebook page, signed by her family, read: "Dear friends: Maria has left us.
"She had to go to heaven like all angels. We are thankful to God for the extra year and a half that he left her with us."
With the news breaking in the paddock in Suzuka just as the second practice session for the Japanese Grand Prix had concluded, Marussia declined to comment.
A spokesperson said: "We have only just heard the news and we are awaiting to find out more.
"We will comment at an appropriate time. If the reports are true, then it is obviously very tragic."
Members of the motorsport community took to Twitter to pay tribute to the young driver.
A message from Sauber F1 team read: "We are shocked to hear about the death of Maria de Villota. Our sincerest condolences and sympathy to her family for this tragic loss."
Caterham F1 Team added: "We'd like to echo the thoughts of the whole paddock and express our deepest condolences on the news of Maria de Villota's passing. RIP."
Former F1 driver Karun Chandhok wrote: "Tragic news about Maria de Villota. Sat next to her just a couple weeks ago at FIA Drivers Comm meeting. Was doing a lot for women in racing."
Sahara Force India added: "Very sad news coming from Spain about brave Maria de Villota passing away. Our thoughts are with Maria's family and friends in this moment."
Sauber team principal Monisha Kaltenborn, who worked alongside De Villota as an ambassador for the Women in Motorsport commission, paid her own tribute.
"It didn't take her any time at all until she was back (from her accident) and was planning to maybe even drive," Kaltenborn told Five Live.
"But more important for her was to really go out there and give other people the courage that you can still do so much, even if you have such a major setback.
"She's been one of the pillars of the work the FIA ambassador programme has been doing, because when you go out there you need to have credibility, a strong personality and you need to be able to reach out to people and that's all she could do.
"She had such a tragic experience and yet she had all that courage to be out there and talk about it and still to believe in that cause, and she always had that smile on her face."
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