In an order filed Wednesday, Sotomayor ruled that the owners of the Hobby Lobby craft store and the Mardel Christian bookstore chains did not qualify for an injunction while they challenge requirements of the Affordable Care Act. The law takes effect Jan. 1.
Sotomayor ruled on the petition because she oversees the federal circuit where Hobby Lobby filed suit challenging the HHS mandate.
The companies' Oklahoma City-based owners contend that the mandate violates their religious beliefs because some of the drugs they are required to cover can lead to abortion.
The family-owned companies have said they have no moral objection to "the use of preventive contraceptives" and will continue to cover those for employees.
The owners have appealed lower-court rulings that denied their claims on religious grounds.
Sotomayor's decision does not pertain to any of the other lawsuits filed by Catholic and other religious organizations against the mandate.
The justice said it is not "indisputably clear" that the companies' owners deserve the injunction while their appeals are pending.
"Even without an injunction, the applicants may continue their challenge to the regulations in the lower courts," Sotomayor wrote in her order, leaving the door open for a future hearing by the Supreme Court.
The request to Sotomayor was the latest legal step by the companies controlled by Oklahoma City billionaire David Green and his family and follows a Nov. 20 ruling by a federal judge in Oklahoma City, who denied a request for an injunction against the mandate.
That decision was appealed to the U.S. Court of Appeals for the 10th Circuit. Lawyers asked for "emergency relief" from fines of more than $1 million a day the companies say they will face if the mandates are not met.
The HHS mandate has a narrow exemption that applies only to those religious institutions that seek to inculcate their religious values and primarily employ and serve people of their own faith.
The mandate does not include a conscience clause for employers who object to such coverage on moral grounds.
About 50 Catholic dioceses, universities and church entities nationwide have filed lawsuits against the mandate.