Biagiotti suffered a heart attack at her home on Wednesday and was rushed to Rome's Sant'Andrea Hospital.
Doctors were able to resuscitate Biagiotti, but she suffered irreversible brain damage.
Lavinia Biagiotti Cigna announced her mother's death in a tweet on Friday, citing a passage from St John's Gospel.
"In the house of my father there are many places. If not, I would have told you. I am going to prepare a place for you," she wrote.
Biagiotti had a career in design for over half a century, and was famous for conquering global markets with her feminine clothing and deluxe knits.
Born in Rome on August 4, 1943, Biagiotti began designing in the 1960s at her mother’s atelier after graduating in archaeology.
She started gaining traction in the 1970s with her voluptuous silhouettes and a palette dominated by white and red - two colours inspired by her city.
Biagiotti initially worked with well-established fashion houses such as Emilio Federico Schubert, Roberto Capucci and Rocco Barocco.
Her first solo collection debuted in Florence in 1972, winning over the press and buyers.
In 1988, Biagiotti became the first Italian designer to stage a fashion show in China.
She also became the first to debut a collection inside the Kremlin walls in Moscow in 1995.
A staunch promoter of Italian fashion worldwide, Biagiotti celebrated 50 years in fashion in 2015 at Milan Fashion Week.
"The oxymoron of fashion, as that of nature, is extracting the eternal from the ephemeral", she said at the time.
Since 1980, Biagiotti had lived and worked in the countryside of Guidonia, near Rome, in the medieval castle Marco Simone, which she restored with her husband Gianni Cigna.
Her husband, who was also her business partner, died of leukaemia in 1996.
Their daughter Lavinia began working for the family company in 1997, and is now the creative director of the fashion house.
With ANSA
