Mansell spun his Ginetta-Zytek and hit the security barrier before the Indianapolis turn. He spent several minutes in his car but was conscious when he was evacuated in an ambulance. Organizers later said he was in a good condition.
The 56-year-old British driver was racing for the first time at Le Mans, with his sons Greg and Leo. Mansell won the F1 title in 1992.
Peugeot took an early lead with its cars holding the four top positions before the safety car entered the 8.45-mile circuit de la Sarthe.
The race was put on hold for about half an hour before Frenchman Franck Montagny moved into first place in the No. 2 Peugeot 908 HDI when Pedro Lamy pitted for the first time in the No. 3 Peugeot.
After 20 laps, Lamy was second ahead of Marc Gene, driving the No. 1 Peugeot.
Nicolas Lapierre of France was fourth in the team Oreca's Peugeot ahead of Scotland's Allan McNish in the No. 7 Audi R15.
Peugeot is bidding for a second straight victory at Le Mans. The French manufacturer ended Audi's five-year domination at Le Mans last year when it claimed its first win since 1993.