The Wyoming bill, which was passed by the state's Republican-controlled legislature earlier this month, makes it illegal to "prescribe, dispense, distribute, sell or use any drug for the purpose of procuring or performing an abortion".
The law is scheduled to take effect on 1 July.
It does not cover morning-after pills or treatment to protect a woman whose health or life is in danger.
It also exempts treatment of a "natural miscarriage according to currently accepted medical guidelines".