Aides to the "first girlfriend" told AFP she had been admitted on Friday "for a rest and to undergo some tests," and was expected to leave hospital on Monday.
Closer magazine reported in its edition published on Friday that Hollande, 59, has been having an affair with actress Julie Gayet, 41.
The weekly glossy printed photos which it claimed showed Gayet and Hollande arriving separately at a flat near the presidential Elysee Palace for secret tryst.
Hollande was reportedly delivered to the flat on a chauffeur-driven scooter and had freshly-baked croissants delivered to the love nest in the mornings by his personal bodyguards.
The Socialist leader has slammed Closer's report as an outrageous attack on his right to a private life and said he is considering legal action.
But he has not denied the substance of the magazine's claims about a passionate affair which pushed him and Gayet to take "insane risks."
Trierweiler, 48, is a glamorous, twice-divorced career journalist who has three children of her own and has been Hollande's partner for the best part of a decade.
Exactly when they became a couple is unclear but most accounts of his turbulent love life concur that he left Segolene Royal, a fellow heavyweight in the Socialist Party and the mother of his four children, in 2005.
In public he was still pretending to be with Royal two years later when she ran unsuccessfully as the Socialists' presidential candidate.
The latest revelations about Hollande have been gleefully seized upon by the media in neighbouring Britain, where the portly and balding president's apparent ability to have numerous beautiful women competing for his attention has long been a subject of fascination and derision.
But in France, the media response was muted and largely restricted to low key factual accounts of what Closer had reported.
Voters too appear to be unfazed by the revelations. A poll published by Sunday newspaper Le Journal du Dimanche (JDD) found that 77 percent of those surveyed agreed with the statement that the alleged affair with Gayet was a private affair that was nobody's business but Hollande's.
Pollsters also say the suggestion that Hollande may have been cheating on his long-term girlfriend is unlikely to have any impact on his standing with the electorate.
"In fact he is already so unpopular that this will not change anything," Frederic Dabi of pollsters Ifop told the JDD.
Hollande is due to give an extended press conference on Tuesday at which he was expected to elaborate on a New Year message that has been interpreted as signalling a change of direction by his government towards more business friendly policies. That event now looks certain to be overshadowed by the turmoil in his private life.
Trierweiler has herself endured a torrid time since entering the Elysee alongside Hollande in the summer of 2012.
At the time she boldly declared that she intended to redefine the role of first lady to the point that they'd have to come up with an alternative term.
An appearance in spiky high heels and a thigh-revealing dress prompted Britain's Daily Mail to exclaim that she was the real star attraction in the couple, the epitome of the "effortless Parisian chic that makes French women the envy of the world."
Within a few weeks however Trierweiler's feisty temperament had got her into hot water.
Reportedly enraged by Hollande's support for Royal, Trierweiler sent out a tweet backing a renegade Socialist candidate who was up against her lover's ex in a battle for a parliamentary seat.
The rebel won and Trierweiler was publicly rebuked by Hollande while his four children reportedly stopped talking to her.
A string of articles and books have portrayed the journalist as a tempestuous, jealous personality who keeps Hollande on a tight leash and polls have suggested two thirds of voters have a negative opinion of her.