The men from Afghanistan and Pakistan were trying to get onto a train overnight Monday at the entrance to the tunnel near the northern French port city of Calais when they were hit by an electric discharge, they said.
The Afghan man was seriously injured, while the two Pakistanis were slightly hurt.
Intrusions into the undersea tunnel have risen in recent weeks as increasingly desperate migrants seek new tactics to enter Britain.
Last week, a migrant was found dead in the tunnel, in what police believe was a failed attempt to climb onto the fast-moving shuttle train that takes road vehicles to Britain.
And late last month, a migrant from Ethiopia died near the tunnel entrance as he also tried to board a train.
Thousands of migrants are camped out around the port in Calais, in the hope of climbing aboard lorries travelling to Britain on ferries or entering the nearby Channel Tunnel.
The migrants, whose presence has long caused friction between London and Paris, sometimes go to dramatic lengths to smuggle themselves into Britain, and have even been recorded trying to swim across the Channel.