Amara, who is also a campaigner for women's rights, told France Inter radio: "I'm not OK with this DNA business because I think we are touching something that is not good for our country.
"Speaking as an immigrant's daughter, I've had enough of seeing immigration exploited all the time, for very clear reasons. I think it's disgusting," she said.
"I am a free woman, never forget that. Quite frankly, the day it really becomes unbearable, the day it gets too hard, I will leave [the government]."
The proposal to introduce DNA testing for potential immigrants to France is part of wider immigration bill that has been approved by both houses of parliament.
It was heavily amended in the upper senate following opposition from across the political spectrum, as well as from religious leaders and rights groups.
The bill now has to go before a joint committee of politicians who will draft a compromise version.
The test would be voluntary and would be conducted when officials have doubts about birth and marriage certificates.
But critics say the bill would set a dangerous precedent by making genetic affiliation a criterion for citizenship.
The government says the test would make it possible for would-be immigrants to speed up the application process.
They point out that 12 other EU countries conduct similar tests.
Patrick Devedjian, the secretary-general of Sarkozy's ruling UMP party, said Amara should not "insult the members of the ruling majority".
Francois Goulard, a member of the UMP who opposed the DNA bill, asked what Amara was "doing in this government".
"If you think the behaviour of some government members is disgusting, there is only one course of action: to leave."
Alpha Oumar Konare, the head of the African Union, has said the proposed DNA tests were "unacceptable at an ethical, moral and cultural level" while Abdoulaye Wade, the Senegalese president, said they were "not respectful of human freedom".