Sotomayor acted late New Year's Eve, just hours before major provisions of the Affordable Care Act law were to take effect.
Sotomayor gave the US government until early Friday morning to give the court its response in the matter.
Her order late yesterday applied to the Little Sisters of the Poor and other Roman Catholic nonprofit groups that use a health plan called the Christian Brothers Employee Benefit Trust, according to the New York Times.
The landmark Affordable Care Act (ACA) legislation was a bid by Obama to guarantee that uninsured Americans are afforded access to medical care, but opponents have objected strongly to various aspects of the law.
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The birth control requirement has been one of the most controversial aspects of the US health law, and has received spirited pushback from religiously affiliated organisations.
The lawsuit by the nuns was one of many challenging the federal requirement for contraceptive coverage.
The November announcement that the Supreme Court would hear the constitutional challenge to the birth control mandate in Sebelius vs. Hobby Lobby Stores Inc., as well as another case, signaled a new phase of the political battle over the health care law.
A decision on the merits of that case by the full Supreme Court could have broader implications, the legal experts have said.