The world-famous tourist attraction, which was visited by six million people last year, was closed on Friday and would remain so on Saturday, officials announced.
Ice has made the stairs and platforms dangerous and salt cannot be used to clear it because it would corrode the iron the structure is made from.
Parks like the Tuileries Gardens by the Louvre Museum were also closed.
As the snow left from this week's heavy fall turned to ice, another three to seven centimetres fell on Friday, not only on Paris but on much of the north-west of the country.
Most motorists followed official advice to leave their cars at home but, although public transport was packed, there was little disruption on the métro and rail network or at airports.
That was not the case for heavy goods vehicles, which were banned from the roads from 5.00am, as they had been earlier in the week.
Some 1,000 trucks were parked up and unable to move on Friday, leading some factories to close for want of material and some shops short of goods.
The ban will be lifted as soon as possible, officials said, in response to complaints from road hauliers about late notice and a lack of coordination.