Tourists, including people dining on the second level, said on French TV that they had been ordered to evacuate when it was learned that someone was scaling the monument.
According to reports, police have arrived at the scene and are negotiating with the man.
A man who climbed the Eiffel Tower on Monday was taken into custody by police after reaching the top.
Police cordoned off several streets closest to the tower as crowds of onlookers gazed up at the perilous operation which began mid-afternoon. Officials haven't immediately provided further information about the incident, and it's not known when the Eiffel Tower will reopen.
"We are at the top and not allowed to leave".
"We kindly advise our visitors to postpone their visit", the SETE added on Twitter. His motivation for climbing the 1,000ft (300m) tower was unclear.
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The incident began at approximately 2:15pm local time.
The ordeal comes days after the city of Paris celebrated the Eiffel Tower's 130th anniversary.
"We are sorry for the inconvenience".
The Eiffel Tower has been closed after a man was seen climbing up its side.
Live television images showed one specialist fireman and another rescuer perched on the 324-metre tower's wrought-iron struts, just below the highest viewing platform trying to persuade the man to give himself up.