A ministry official said Julie Gayet, who is reported to be pregnant, had been nominated for a place on the jury at the Villa Medicis, a French state-owned institution in the Italian capital Rome.
However, Culture Minister Aurelie Filippetti rejected the nomination without giving a reason.
Yesterday's decision came a day after Mr Hollande held a news conference in which he admitted to problems in his love life but refused to comment on the alleged affair.
Mr Hollande's First Lady, journalist Valerie Trierweiler, has been in hospital since Friday, when Closer magazine published photos it said proved Mr Hollande's liaison with Gayet.
According to some French media reports, the 41-year-old actress is four months pregnant with the president's baby.
Ms Trierweiler, 48, has been in hospital suffering from "extreme shock" over the affair revelations and may be there for more than a week.
In Tuesday's press conference, intended to unveil plans to re-energise the country's economy, Mr Hollande made no mention of his partner of seven years, refusing to say whether she was still First Lady and furiously denouncing questions about his love life.
But he did say he would clarify whether Ms Trierweiler was still First Lady before a trip to America on February 11.
Asked about her health, Mr Hollande said she was resting and that he had no further comment to make.
The First Lady does not have formal status in France, but in practice she has an office in the presidential palace and small staff.
The president has left open the possibility of suing Closer magazine. The French media face strict privacy laws but the tradition of secrecy over the private lives of public figures has been eroded in recent years.