Ms Bachelot said promoting anorexia was not freedom of expression
The French National Assembly has passed a groundbreaking bill which seeks to criminalise the promotion in the media of extreme thinness.
The bill targets pro-anorexia websites and publications that encourage girls and young women to starve themselves.
It will affect websites, fashion houses, magazines and advertisers.
If approved by France's upper house, those found to have encouraged severe weight loss could be fined up to 45,000 euros and face three years in prison.
French Health Minister Roselyne Bachelot said the proposed law would help stop advice on how to become ultra-thin being spread through pro-anorexia sites on the internet.
"Encouraging young girls to lie to their doctors, advising them on foods that are easier to regurgitate and inciting them to beat themselves up each time they eat is not freedom of expression," Ms Bachelot told the assembly.
"These messages are death messages. Our country must be able to prosecute those who are hiding behind these websites," she said.
Jacques Domergue, a lawmaker supporting the bill, said that the intention was to send a strong message to society.
"It is necessary because we know now that we have a risk to some part of the population, young girls, who are pressed by different types of lobbies and the risk is increasing."
The law could also affect the fashion industry and magazine editors who publish photographs of extremely thin models.
If the bill is passed by France's upper house, the Senate, in the coming weeks offenders could face jail sentences of up to two years and 30,000 euros ($47,387; £23,980) in fines.
A three-year term and 45,000 euros in fines could be sought against offenders if the incitement was found to have lead to death.
The BBC's Emma Jane Kirby in Paris says that with 40,000 anorexics in France, many parliamentarians feel the law cannot come soon enough.