Ms Trierweiler left the Pitie Salpetriere hospital for a presidential residence at La Lanterne in Versailles, the magazine Paris Match said.
She was admitted to hospital apparently in shock after learning of the reports.
Closer magazine had alleged the liaison between Mr Hollande and Julie Gayet.
It said that the affair had begun during the 2012 presidential race.
Ms Gayet, 41, says she is suing Closer for breach of privacy, seeking 50,000 euros (£41,000; $68,000) in damages and 4,000 euros in legal costs.
Ms Trierweiler, 48, works for Paris Match, which said she was planning to rest at the residence.
Mr Hollande has not commented on the latest news.
However, a source at the presidential office told Agence France-Presse news agency that Ms Trierweiler would rest at La Lanterne "for a few days".
Ms Trierweiler was admitted to hospital on 10 January.
Mr Hollande visited her for the first time on Thursday evening.
French media have claimed that Ms Trierweiler suffered an anxiety attack last week, but her friends have played down her condition.
At his annual news conference on Tuesday at the Elysee to discuss his political agenda, Mr Hollande was asked questions about the alleged affair.
Mr Hollande, 59, said he was experiencing a "difficult moment" in his private life but refused to answer questions over the report in Closer, saying "private matters should be dealt with privately".
Nor would he clarify whether Ms Trierweiler was still first lady before a February trip to the US.
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