The Sudanese man was arrested close to the British entrance and “almost succeeded in walking through the tunnel”, a spokesman for owner Eurotunnel told BBC News.
A spike in the numbers of migrants trying to make the crossing has become a sensitive political issue in Britain, and the story was splashed across the front pages of Friday's newspapers.
A spokesman for Britain's Home Office said it had improved security by paying for more fencing at the French side and drafting in border guards and dogs.
“We continue to work closely with the French government and Eurotunnel to tackle the immediate pressures and longer-term issues involved in the situation in northern France,” the spokesman said.
Police in Kent, the county where the tunnel emerges, said that 40-year-old Abdul Rahman Haroun had been arrested and charged with causing an obstruction to an engine or carriage.
The Daily Telegraph reported that ministers were considering closing the tunnel to freight and passenger trains at night in response to the crisis.
Eurotunnel did not immediately respond to a request for comment.