The incident took place at about 2am local time, the official said, adding that the victim was thought to be from Eritrea or Sudan. At least 10 people have died in or near the tunnel since late June.
About 3,000 people, mostly from Afghanistan, Syria and African countries, are living in camps in Calais near the Channel tunnel entrance. They have made repeated attempts to reach the UK, often by trying to enter the tunnel or climb on to lorries.
In July, Eurotunnel said 2,000 attempts were being made a night to get into the tunnel, but new fences erected around the tracks, as well as a increased police presence, have greatly reduced this number.
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