A cordon surrounded the area as officers stopped people from getting close to the landmark.
A spokesman for police in Paris said: "A person was arrested, the incident is finished. He wasn't armed. We'll know more about his motives tomorrow."
Bob Thomas said on Twitter: "Anyone know what is going on at the Eiffel Tower? All been shut down."
Earlier in the evening the tourist told the Mirror: "We're stuck in one of the legs outside the lift. We've been locked in.
"Told it's a full lock down. Nothing official yet."
"We are currently locked down at the base outside one of the lifts. Been told a guy was acting weird but no confirmed weapon. The staff have been locked in with us."
The incident came as another security scare unfolded at the Gare du Nord, where passengers on the Eurostar were evacuated when a "suspicious item" was found.
Zoë Grisedale said: "They have found a suspicious item. We are all to wait outside terminal."
Eurostar said on social media: "We regret that for security reasons check-in and border controls will need to be repeated for customers of #ES9063.
"There will be a consequent delay to the departure of #ES9063. Thank you for your understanding."
Paris-based journalist Charlotte Dubenskij said the Eiffel Tower is now open again.
Just a few weeks ago police arrested a knife-wielding man wearing a Paris Saint-Germain football shirt after he tried to breach security at the Eiffel Tower.
France has been the victim of a string of ISIS-inspired terror attacks in the past two years, most notably the November 2015 atrocities which claimed the lives of 130 people.
Last year, Nice truck terrorist Mohamed Lahouaiej Bouhlel killed 86 people and injured 434 when he drove his truck into a crowd celebrating Bastille Day.
