Justices granted the request of Attorney General Steve Marshall to stay a judge's order striking down the law , Marshall's office announced.
"The Supreme Court's stay allows the Alabama Memorial Preservation Act to remain in effect until the Supreme Court resolves this appeal over the act's constitutionality," Marshall said in a statement.
Marshall said he believes a judge erred when he ruled the law unconstitutional.
The 2017 Alabama Memorial Preservation Act prohibits relocating, removing, altering or renaming public buildings, streets and memorials that have been standing for more than 40 years. Cities can be fined for violations.
Jefferson County Circuit Judge Michael Graffeo last month ruled that the law violates the free speech rights of local communities and declared it void.
The state law doesn't specifically mention Confederate monuments, but it was enacted as some Southern states and cities began removing such monuments and emblems.
Alabama sued the city of Birmingham in 2017 after officials erected a wooden box that obscured the view of a 52-foot-tall (16-meter-tall) obelisk honoring Confederate veterans.
In his order declaring the law unconstitutional, Graffeo said it was indisputable that most citizens in the majority black city are "repulsed" by the memorial. He rejected the state's claims that lawmakers had the power to protect historical monuments statewide.
Justices on Friday also agreed to stay any fines against Birmingham as the court case plays out over the law's constitutionality.