WASHINGTON—A federal judge ordered the Pentagon to halt work on the massive JEDI cloud-computing contract, handing Amazon.com Inc. an early win in its efforts to overturn the award to rival Microsoft Corp.

Judge Patricia Campbell-Smith of the U.S. Court of Federal Claims issued the preliminary injunction on Thursday to block the Pentagon from proceeding with the contract, “until further order of the court,” according to a court docket entry. The judge’s order itself remains sealed temporarily.

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