Indiana is asking the U.S. Supreme Court to review a case that could lead to a substantial rollback of abortion law.

The state Oct. 12 filed a petition asking the high court to overturn an appeals court decision that struck down its discrimination abortion law—a provision it said prevents women from selectively terminating fetuses based on sex, race, or disability.

The U.S. Court of Appeals for the Seventh Circuit invalidated the discrimination provision and one that sets out requirements for...