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.
Cyclist Daan Myngheer, 22, has died in hospital after suffering a heart attack during the first stage of the Criterium International in Corsica.