Around 90,000 people packed into a specially-designated fan zone at the foot of the monument to watch Portugal beat France 1-0 in Sunday's Euro 2016 final.
Police used tear gas outside the fan zone, however, when a small group of people tried to force their way in despite being told the venue was already full to capacity.
On Monday the group that manages the Eiffel Tower said it could not open in "proper security conditions."
The fan zone was full by 7 p.m. local time, two hours before kick off, and riot police later used tear gas on a small group who had thrown objects at them.
A water cannon was also deployed as troublemakers set fire to rubbish, scooters and least one car in the area.
Nine people were in custody in Lyon for engaging in similar behaviour.
Keeping France safe was a task involving tens of thousands of security forces in 10 cities. For Sunday night's final, there were 1,900 police in the fan zone near the Eiffel Tower.
Thousands more were deployed on the Champs-Elysees and at the Stade de France, one of the venues hit in November's Paris attacks that killed 130.