They report the threats as they consider tougher restrictions on unvaccinated people in France.
Several French MPs say they have received death threats as they debate a Covid-19 pass that would bar the unvaccinated from much of public life.
The government is seeking to pass a law that would require people to show proof of vaccination to access public venues and transport with some exceptions.
The legislation is expected to be approved in a vote this week but has angered vaccine opponents.
France has one of the highest Covid vaccination rates in the EU.
At least 91% of the adult population have been fully jabbed, according to the French government.
On Sunday Agnès Firmin Le Bodo of the centre-right Agir party tweeted an email she received containing graphic threats to kill her over her support for the vaccination pass.
“Our democracy is in danger,” wrote Ms Firmin Le Bodo, who is also a pharmacist and vaccinates people against Covid.
In an interview with BFM TV, she said she had reported the threats to the police and would not be deterred from supporting the vaccine pass.
Another MP, Naïma Moutchou of the Horizons party, shared a similar tweet which included a screenshot of an emailed threat.
In parliament on Monday, Health Minister Olivier Véran condemned the death threats and the “selfishness” of vaccine opponents.
Last week Interior Minister Gérald Darmanin said police would strengthen protections for elected officials ahead of the vote on vaccine passes.
Barbara Bessot Ballot of the ruling En Marche! party said MPs had received messages threatening to kill them for “attacking our freedom”.
“Those death threats are unacceptable,” she wrote on Twitter.
Throughout the pandemic, critics have accused French President Emmanuel Macron’s government of violating freedoms by imposing Covid rules. Protests against these rules have been held regularly.
For months France has asked people to show either proof of vaccination or a negative Covid test to access many public venues.
But the French government has decided to remove the option to show a negative test in response to record increases in infections, driven by the highly contagious Omicron and Delta variants of Covid.
The government is aiming to bring the vaccine pass into force in mid-January, once it has been approved by parliament.
Most parties back the vaccine pass, which is expected to be passed by the lower house early this week, before being debated in the Senate on Wednesday.