Reuters reported that the court would hear the appeal by the Trump administration against a ruling by a lower court last year.
A ruling is due by the end of June 2018.
In July 2016, the US Court of Appeals for the Second Circuit based in New York reversed a decision by a Southern District of New York court which had held Microsoft in contempt of court for refusing to hand over the customer emails.
The Department of Justice said in its appeal that the lower court ruling “gravely threatens public safety and national security” because it limits the government’s ability to “ward off terrorism and similar national security threats and to investigate and prosecute crimes".
Google is fighting a similar case in which it has received a contrasting ruling.
The company was served a search warrant in July last year and ordered to turn over email stored abroad, which the US said it needed for a federal investigation into wire fraud.
Google contested the warrant, citing the Microsoft case.