The Elysee Palace said that Trierweiler, 49, had suffered a "severe case of the blues" last Saturday after Closer published an article about the alleged affair with Julie Gayet. She was taken to a Paris hospital and was expected to remain until today.
What began as a severe embarrassment for Hollande is turning into a double, personal and political, crisis.
Today was supposed to be the first day of a reinvigorated Hollande presidency - a press conference to unveil details of a promised "acceleration" towards a more market-oriented economic policy.
The acceleration now risks falling flat on its face unless Hollande can find a way to defuse potentially explosive questions about his alleged love affair, Valerie Trierweiler's health and the validity of her status as France's first lady.
Hollande, 59, and Trierweiler are not married. Her semi-official position is based on her private status as "first girlfriend". If she has lost that status, can she still perform the functions?
A close friend of the President told Le Monde: "The President has to make a rapid decision [in favour of one woman or the other]. If he does so, the French will not hold it against him. [Until then] any appearance of Valerie by his side will appear hypocritical ... that would be unbearable."
In one month's time, Hollande and Trierweiler are due to travel to Washington as French first couple to visit the Obamas.
It emerged over the weekend that they were no longer living in Trierweiler's flat in the 15th arrondissement of Paris. Since the northern summer, they have been living in the Elysee Palace. Trierweiler has her own rooms in the eastern wing of the palace. She is, however, seldom seen in the rest of the building.
The President's alleged relationship with the actress Julie Gayet is said to have started almost a year ago, stopped and then resumed since the northern summer.
There have been a series of crisis meetings in the Elysee over the weekend to try to decide presidential tactics. Should a statement be made to "clarify" Trierweiler's position?
Hollande decided to stick by his insistence that "private" and "public" life were separate, even if Closer magazine had smashed the barrier which has traditionally shielded the romantic activities of French politicians from the gaze of the French press. Hollande will respond to questions about the alleged affair at the press conference tonight NZT "if he is asked", Elysee sources said. The President's instinct will be to try to say as little as possible.
An opinion poll yesterday appeared to give public support to Hollande's position. Of a sample of 1025 French people questioned by IFOP for Le Journal du Dimanche, 77 per cent said the alleged affair was a "private matter" which concerned only Hollande. Over 84 per cent suggested that the affair - which has not been denied - would not change their opinion of the President.
As one senior pollster pointed out, Hollande's popularity is already so weak - 22 to 25 per cent, the lowest of any modern president - that it could hardly fall further. That does not mean that the Closer revelations are politically harmless.
They have occurred at just the moment that the President has signalled he is ready to adopt market-oriented reforms in an attempt to revive a stumbling French economy. To push through such reforms against the left of his own party will demand the deployment of all of Hollande's remaining personal and political authority. Trierweiler's collapse risks making him seem heartless. The pictures in Closer risk making him seem incautious and even ridiculous.
The press conference was a risky affair in any case. In his New Year's message, Hollande offered a "responsibility pact" to French employers. He said that he would cut the high payroll taxes, or social charges, which fund the French welfare state if employers would guarantee to create jobs.
He is expected to offer details of this pact. "If he goes towards a 'pro-bosses' policy, he risks cutting himself off from part of his base ..." one senior Socialist politician said. "If he is vague or pulls back, he will confirm his reputation for weakness and indecision."
- Independent, with additional reporting by AP