A person could be seen dangling just below the third and highest level of the structure. A rescuer dressed in red was just above him.
Police said the climber was a male.
It wasn't immediately clear how the trespasser managed to get past the stringent security system.
A Paris police spokeswoman said a team of firefighters including a climbing specialist was on the scene and in touch with the intruder, whose motivations remain unclear.
Officials haven't immediately provided further information about the incident, and it's not known when the Eiffel Tower will reopen.