The South Dakota law – approved by the governor on Monday – makes it a crime for doctors to perform terminations.
Exceptions will be made if a woman’s life is at risk, but not in cases of rape or incest.
Many believe new appointments to the Supreme Court may have tipped the balance in favour of anti-abortionists. The supporters of the South Dakota law say they want to trigger a battle over the 1973 Roe-versus-Wade ruling, in which the US Supreme Court established that governments lacked the power to prohibit abortions.
Under the law signed by South Dakota Governor Mike Rounds, doctors could get up to five years in prison and a $5,000 (Â£2,800) fine for performing an illegal abortion.
State proposals to ban abortion are before legislatures in Mississippi, Georgia, Indiana, Missouri, Ohio, Kentucky and Tennessee.
(My American readers may want to check in with our friends at Planned Parenthood.)