In a brief order, the court granted a request by abortion providers seeking to reinstate a lower-court injunction that blocked the law, which required doctors to obtain a formal affiliation with a local hospital.
The order noted that one of the eight justices, conservative Clarence Thomas, said he would have denied the application.
The order said the court's action was in line with its decision in June to temporarily block part of a Texas abortion law that was challenged by abortion providers in a high-profile case. The eight justices heard oral arguments in that case on Wednesday.
The Louisiana law mandates that physicians who perform abortions have "admitting privileges" at a hospital within 30 miles (48 km) of the facility where abortions are performed. The regulation matches one in the Texas law.
