"The current situation does not permit us to open under adequate safety conditions," said a spokesman for the company that operates the tower, one of the world's most popular tourist attractions, and under which tens of thousands watched the final on giant screens on Sunday night.
French police arrested 40 people overnight after the Eiffel Tower fan zone reached its 90,000-capacity, leaving some frustrated at being unable to watch a match that France ultimately lost 0-1 to Portugal.
Police used tear gas and water cannon to disperse the crowd, and firefighters were called in to deal with a car and a scooter set ablaze during the trouble.
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Nevertheless, Interior Minister Barnard Cazeneuve told a news conference the month-long tournament, involving dozens of matches and millions of fans, had gone off smoothly despite some fan violence, notably battles between Russian and British fans in the port city of Marseille early on in the tournament.
France has been under emergency rule since Islamist militants killed 130 people last November in multiple attacks on Paris and outside the Stade de France stadium where the final match was played on Sunday night.
Fears of an Islamist militant attack on the competition prompted heightened security measures, but officials had resisted calls to ban the fan zones in Paris and elsewhere.
"France was able to remain France," said Cazeneuve, adding that the country nevertheless remained on maximum security alert.
The security focus would now turn away from football to a Tour de France cycling race and the summer season of open-air festivals across the country of 65 million people, he said.
In all, 1,550 people were arrested by police during the Euro 2016 football tournament, with 64 expelled from the country and 59 sentenced to jail or given suspended jail terms for various offences, he said.
(Reporting By Brian Love and Marine Pennetier; Editing by Andrew Callus)
