The Musée d'Orsay, on the opposte bank of the river, also closed early on Thursday night as a precautionary measure.
The Louvre will remain closed on Friday to allow staff to evacuate tens of thousands of “reserve” paintings and sculptures in its underground store rooms.
Fears had been growing all day of serious flooding in Paris as the European football championship approaches – despite official assurances that all should be well.
As scores of towns to the east and south of Paris suffered their worst flooding for decades, the river Seine rose above its “preliminary” alert level of 5 metres on Thursday afternoon.
The Seine quays were awash. A popular island near the Eiffel Tower was submerged. Pleasure launches and commercial barges were banned from passing through the French capital.
Elsewhere, a motorway slip-road in eastern Paris was inundated and closed, and services on a suburban railway line which hugs the left bank of the Seine, RER C, were suspended.
François Duquesne, head of Vigicrues, the agency which monitors water levels in France, said: “The Seine is still rising but we are far from the 8.5 metres recorded in 1910 (when large areas of the capital were flooded for 45 days). We should see a rise to a peak of around 5.6 metres overnight.”
The flood alert level in Paris is at yellow, the third highest but is expected to be upgraded to orange shortly.. One department just east of Paris, Seine et Marne, is on “red alert”, the highest level. Several other departments within the Seine catchment area are at the “orange” or second highest alert level.
Other experts warned that the weather and flood levels remained unpredictable, a week before the Euro 2016 national football tournament begins in Paris next Friday. A giant “fan zone”, capable of hoisting up to 100,000 people has been built on the Champ de Mars, beside the Eiffel Tower and close to the river.
Flooding approaching the 1910 levels would put the fan zone under water.
In its emergency plan the Louvre has 72 hours to remove works in its underground reserve. The Musee d'Orsay has 96 hours. Both museums held drills this year to deal with floods.
In March the Louvre evacuated the whole of the underground section of its Islamic art galleries in a day.
The floods in other parts of northern France claimed a second victim on Wednesday night when the body of an 86-years-old woman was found in her home. A toddler was drowned in Burgundy last weekend.
The Prime Minister, Manuel Valls and interior minister Bernard Cazeneuve visited Nemours, 80 kilometres (50 miles) south of Paris, whose town centre has been completely evacuated. President Francois Hollande declared a “natural catstrophe”.
“In 60 years of living here I have never seen this,” Sylvette Gounaud, a shopworker in the town, said. “The centre of town is totally under water, all the shops are destroyed.”
The main A10 motorway from Paris to the south west remains flooded north of Orléans. On Wednesday, 650 motorists and truckers were stranded after the motorway turned into a river. Amphibious army trucks were sent to rescue them.
In a diagonal band of territory from the Bay of Biscay to the Belgian border, rainfall in the month of May was two and a half times the normal level.
A catastrophic Paris flood is overdue. The last occurred in 1910 and the city has been flooded by the Seine on average once a century.
The latest weather forecasts suggest that a spell of drier weather should begin this weekend.
The bad weather has added to disruption caused by a series of strikes which began last week but the industrial action appears to be weakening.
Air traffic controllers abandoned a planned three day stike over the weekend. An indefinite rail strike entered its second day but one of the three union federations involved pulled out.
A partial strike on the Paris Metro had no significant effect on services. Strikes at nuclear power stations caused electricity cuts in some areas.
The industrial action is partly linked to a confrontation between militant unions and the government over reform of unemployment law. Rail and aviation unions also have their own specific grievances.
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