Valérie Boyer, a member of the governing UMP party, was successful in getting parliamentary approval for a bill that outlawed the denial of a massacre of Armenians by Ottoman troops in 1915.
The bill’s passage unleashed a wave of indignation in Turkey.
Turkish prime minister, Recep Tayyip Erdogan, said the vote represented “politics based on racism, discrimination and xenophobia.”
Daily newspaper Le Parisien reported that Boyer’s website was attacked on Sunday.
Visitors were redirected to a site showing the Turkish flag and a message attacking the French government and the Armenian community in France.
“You, the Armenian diaspora, are so cowardly that you don’t have the guts to open up the archives and face the truth,” said the message.
In an attack on French politicians the message said “you, the French, are so pitiful and pathetic that you ignore the truth to get votes.”
On Monday morning, the site, valerie-boyer.fr, was still unavailable with a "site indisponible" message being shown.
Boyer said she has received numerous “insults and threats of murder and rape” over recent days on her Facebook page and her Twitter account.
“That such a level of violence is being expressed shows the necessity to punish genocide denial,” she told the newspaper.
“What I’m experiencing is without doubt nothing compared to the experience of the Armenian community."
Turkish vice president Ali Babacan has also accused President Nicolas Sarkozy of reneging on a promise not to introduce such a law.
“I heard this promise personally during meetings we had,” he said. “What happened last week then? Where is the promise?”
The bill will now go to the French parliament’s upper house, the Senate. If passed, it could become law next year.