The veteran designer suffered brain damage following a heart attack late on Wednesday, and died early on Friday, the AGI agency said.
The Laura Biagiotti brand is known for its fine knitwear and loose clothes as well as perfumes, accessories and watches.
Dubbed the "Queen of Cashmere", her company said it uses 50,000 kilogrammes (110,000 pounds) of the fine soft wool every year to make its clothes.
She was also one of the first to market Western collections to other parts of the world, staging fashion shows in China in 1988 and in the former Soviet Union in 1995.
In a 2015 interview to mark her 50 years in the industry, she said that fashion could play a role in changing societies.
"In China, in 1988, we understood that after so many years of which clothing had united, unified women and men, they all wanted to express their own individuality," she told the business newspaper Il Sole 24 Ore.
She began her career in 1965 when she joined her mother Delia, who had just opened a dressmaking business in Rome after having designed uniforms for the crews of the Alitalia airline. The young Laura launched her first collection in Florence in 1972.
Along with a group of other designers, such as Ottavio Missoni and Gianfranco Ferre, she helped move Italy's fashion capital from Florence to Milan.
Since 1980 she had lived and worked in a restored 11th-century castle near Rome with her husband Gianni Cigna, who died in 1996. Her daughter Lavinia is the vice president of the group.
She was also known in Italy as a strong supporter of the arts and sponsored the restoration of numerous historic buildings. The Biagiotti group stages more than 70 shows every year.