A trigger law outlawing abortion would take effect 30 days after Roe v. Wade was overturned.
An older law could criminalise abortions, but it's unclear if it still applies.
In Texas, abortion is legal up to six weeks of pregnancy. Uncertainty surrounds the Supreme Court's decision in a landmark abortion rights case.
The state already has the nation's most restrictive abortion law, prohibiting the procedure when many women are unaware they are pregnant and enforcing it by ordinary Texans.
But it also has several laws that would outlaw abortion if the Supreme Court allowed it.
Roe v Wade, the nearly 50-year-old ruling that guarantees a constitutional right to an abortion, is currently before the Supreme Court.
A leaked draught decision in the case, published late Monday by Politico, suggests the court may do just that.
The draught leaves it up to state legislatures or Congress to decide whether abortions should be legal.