In a statement, Chirac wrote: "After some weeks of contacts concerning such a visit, it turns out that it is impossible ... and you are not welcome following your comments."
An Israeli foreign ministry government spokesman refused to comment on "confidential messages".
Sharon sparked anger in Paris with a speech on Sunday in which he urged all French Jews to move immediately to Israel in order to escape what he called the "spread of the wildest anti-Semitism".
The French foreign ministry described the remarks as "unacceptable", and French politicians, media and religious leaders also reacted with indignation, with Jean-Louis Debre of the ruling Union for a Popular Movement (UMP) saying the prime minister had "missed a good opportunity to shut his mouth".
Sharon told a meeting of American Jewish groups in Jerusalem that while he regularly called on Jewish communities around the world to emigrate to Israel, in France "it is a must ... they have to move immediately" because of the hostility towards them from the country's five million Muslims.
Israeli government spokesman Avi Pazner told a French radio station that Sharon had been "misunderstood" and that all he meant was that the place of all Jews was in Israel.
But French Jewish leaders, who have persistently denounced the growing violence against their 600,000 strong community, rallied against the comments, with Richard Prasquier of the Representative Council of Jewish Institutions accusing Sharon of "pouring oil on the fire in an unacceptable fashion".