Race organizers said the 34-year-old Simonsen was taken to the hospital after his Aston Martin No. 95 crashed about 10 minutes after the start of the race. The car spun at high speed and skidded into the barrier at the Tertre Rouge corner where speeds reach up to 170 kph (105 mph).
The violence of the impact showed as a tire from Simonsen's car rolled on the track while a door hung open.
Simonsen died at the hospital soon after arrival "due to his injuries," organizers said.
"Tragically, and despite the best efforts of the emergency services in attendance, Allan's injuries proved fatal," Aston Martin Racing said in a statement on its website.
Sebastien Enjolras lost his life in pre-qualifying in 1997. The last driver fatality in the 24-hour race itself was Jo Gartner in 1986.
The worst crash in Le Mans history occurred in 1955 when Pierre Levegh's Mercedes flew into the crowd, killing more than 80 spectators.
Aston Martin, which has five Vantage V8 cars in the GTE-Pro and GTE-Am classes, will continue in the race "at the specific request" of Simonsen's family and in tribute to the driver.
"I would like to extend our deepest sympathies and condolences to the individuals, and families whose friends or loved ones were involved in today's terrible tragedy," Aston Martin Racing managing director John Gaw said.
The safety car came out after the crash and the race was held up for nearly an hour to repair the guard rail.
Simonsen was participating for the seventh time at the endurance race, which is won by the team that completes the most laps in 24 hours with up to three drivers alternating. He finished second in the GT2 class at Le Mans three years ago. He clocked the fastest time in qualifying on Thursday in the GTE-Am class.
Jean Todt, the FIA president, and Pierre Fillon, president of Le Mans organizer the Automobile Club de l'Ouest, paid tribute to Simonsen.
"Allan was an extremely talented and experienced sports car driver who had raced in every corner of the world and was highly respected by his peers and his team," they said in a joint statement. "For many in endurance racing, Allan was above all a good friend who displayed his passion for racing on and off the track. His loss will be felt by the FIA, the ACO and the greater motorsport family."
Simonsen and Danish co-drivers Kristian Poulsen and Christoffer Nygaard were leading the GTE-Am class in the world endurance championship after topping their category at Silverstone in April and finishing second in Spa-Francorchamps last month.
Audi held the top three spots after the sixth hour, followed by two Toyotas.
IndyCar series leader Helio Castroneves tweeted: "Very sad to know about the fatal accident of Allan Simonsen on Le Mans today. Praying for him and (his) family."
Tony Kanaan, another IndayCar driver, tweeted: "Such a tragic news on the passing of @AllanSimonsen. Sad day in motorsports again. Thoughts and prayers are with his family."
There was second driver death on Saturday, in Germany. Two-time champion Wolf Silvester died because of "health problems" during the German VLN Endurance Racing Championship, race organizers said.
Safety marshalls said Silvester, 55, apparently lost control of his Opel Astra OPC, and when they approached the stopped car on the track they found him sitting motionless in the seat. The dpa news agency reported that Silvester had a heart attack.