At issue is a state law in Louisiana which requires doctors who perform abortions to have admitting privileges at a nearby hospital.
Pro-choice groups argue that the law would severely restrict access to abortion and lead to the closure of two of the three remaining abortion clinics in Louisiana.
The case, June Medical Services v. Russo, will be the first to come before the court since President Donald Trump appointed two conservative justices -- Neil Gorsuch and Brett Kavanaugh -- to the nine-member panel.
"The case is significant because the law that is being challenged is more or less identical to one that the court struck down in 2016," said Mary Ziegler, a law professor at Florida State University.
"Switching court membership? Is that enough to undo a case?" asked Ziegler, author of "Beyond Abortion: Roe v. Wade and the Battle for Privacy."