Davidson's Toyota tangled with a Ferrari sportscar he was trying to lap, hitting the rear and twisting through the air before plunging into the barriers at the entry to the fast Mulsanne straight.
The 33-year-old, an ex-Formula One driver and grand prix analyst for Sky television, climbed out of the number eight car and gesticulated before receiving treatment from the medical team at the Sarthe circuit.
The AF Corse Ferrari landed upside down but Italian driver Piergiuseppe Perazzini was also able to pull himself clear of the vehicle.
Toyota said Davidson was taken to the circuit medical centre and would go to a local hospital for precautionary checks although he was walking and talking normally and did not appear to be injured.
Moments before Davidson's crash, Nicolas Lapierre in the number seven Toyota petrol-hybrid had taken the lead from Audi's number one R18 diesel-hybrid driven by fellow Frenchman Benoit Treluyer.
The pair swapped places more than once before the Toyota racer made the move stick.
With the safety car out on the track, Audi and Toyota then took the opportunity to swap their drivers and Marcel Fassler returned the Audi hybrid R18 to the lead.
Former Formula One driver Kazuki Nakajima slotted into second place in the Toyota ahead of Audi's Italian Rinaldo Capello in a hybrid 1-2-3.
Britain's Oliver Jarvis was fourth in the Audi R18 ultra ahead of the Toyota-powered Lolas.
The second Audi R18 ultra was back up and running in 24th place overall after Romain Dumas put it into the tyre barriers in an earlier crash.
The Frenchman frantically dug the Audi out of the tyre wall and nursed the damaged car back to the pits.
In the LMP2 category, the Morgans of the Oak Racing team held first and second position.
Le Mans debutant Alex Brundle took over from his father, 1990 Le Mans winner and ex-Formula One driver Martin Brundle, and their Zytek Z11SN car was running in 29th.
The GTE class for sportscar manufacturers was led by Richard Westbrook's Corvette Racing car while the innovative Nissan-powered DeltaWing was hampered by gearbox and fuelling problems and fell back to 49th.
The sleek car, reminiscent of a 'Batmobile', was invited to race at Le Mans to showcase new technologies, including a smaller engine and four-inch front wheels, and will not be classified.
Audi won last year's race with a diesel-powered car, their 10th victory in the last 12 years at the event.
This year's race is the 80th edition of the sportscar classic at the Circuit de la Sarthe.