He is the second Belgian cyclist to die in as many days after Antoine Demoitie was struck by a motorbike during Belgium's Gent-Wevelgem race.
Myngheer, who turned professional last year, had been in an induced coma.
His team, Roubaix Metropole Lille, said in a statement: "He lost his last race after fighting like a champion."
Myngheer pulled up in difficulty 20 miles from the line in the first stage of the race at Porto-Vecchio on Saturday.
He suffered the heart attack while in an ambulance, before being transferred by helicopter to hospital, where he was put on artificial respiration and fell into a coma. According to his team, Myngheer's organs have been donated.
British cyclist Mark Cavendish tweeted: "Such a terribly sad few days in the professional cycling world. Another tragic loss.
"RIP Daan Myngheer. My thoughts are with your loved ones."
The Trek-Segafredo team added: "The cycling family loses another young talent. Our thoughts go to the loved ones and team members of Daan Myngheer."
The latest tragedy comes after Demoitie, 25, was killed when he was hit by a motorbike on Monday.
The accident happened after several riders crashed as they passed through northern France during Sunday's Gent-Wevelgem one-day race.
Demoitie, who was riding for the Wanty-Gobert team, was taken to hospital in Lille but died some time later.
In January, six racers from the Giant-Alpecin team, including German John Degenkolb and Frenchman Warren Barguil, were injured in a collision with a car during a training ride south of Valencia.

But pay remains lower than at Aldi and Lidl and overtime pay on Sundays and Bank Holidays is being cut.
Currently Tesco workers are paid £7.62 an hour, which will rise to £8.42 an hour by November 2018.
The pay rise will put Tesco workers' pay above the £7.90 level that the National Living Wage is expected to reach by 2018.
The National Living Wage is the effective minimum wage for adults aged 25 and over, and is currently £7.50.
Those under the age of 25 are entitled to a lower minimum wage rate.
Statutory minimum pay rates will continue to rise until at least 2020, according to recent government Budgets, and companies are planning for those changes, as well as striving to remain competitive with rivals in order to recruit and retain staff.
Wage growth in the UK has been slow in recent years, but inflation has risen and other supermarkets have increased the wages they pay.
Aldi recently announced a rise in hourly pay to £8.53 an hour; Lidl's website says it pays store staff £8.45 an hour.
Tesco said it would increase hourly pay in three stages: to £8.02 in November 2017, then to £8.18 in July 2018 and to £8.42 in November 2018.
"This reward package sees our biggest investment in store pay for a decade, and gives colleagues a sustainable pay deal that rewards them for everything they do, while allowing us to also attract new talent," said Tesco UK chief executive, Matt Davies.
The retailer said maternity pay terms had also been improved. But extra pay for Sundays and bank holidays will be reduced from time-and-a-half to time-and-a-quarter after July 2018.
"This is designed to meet the government legislative requirement around the minimum wage.
"As expected, most of the businesses who have had to face up to this rise have had to reduce premiums and other perks that employees benefitted from in order to meet the core wage rises," said retail analyst Steve Dresser.

The 29-year-old was released by Preston in December and joined Scottish Championship side Hibernian, but was out of contract this summer.
His previous clubs include Shrewsbury and Motherwell, with his deal including the option of a further 12 months.
Meanwhile, Bury goalkeeper Ben Williams, 34, has left the club after making 21 appearances last season.
The former Crewe and Colchester man joined the Shakers from Bradford last summer.
Find all the latest football transfers on our dedicated page.
Cyclist Daan Myngheer, 22, has died in hospital after suffering a heart attack during the first stage of the Criterium International in Corsica.
[NEXT_CONCEPT]
Hourly pay rates for Tesco store staff will rise by 10.5% over the next two years, the supermarket has said.
[NEXT_CONCEPT]
League One club Bury have signed Jamaica international winger Chris Humphrey on a one-year deal.