Booz Allen Hamilton Inc. was one of 13 companies to win part of a $900 million contract to provide the U.S. military with support for its expanding cyber operations, the Defense Department announced Tuesday.

The award comes as Booz Allen is facing increased scrutiny as the company that last hired Edward Snowden, the National Security Agency contractor who used his position to take classified information on the nation’s surveillance programs and leak it to the world media.

The decision by the U.S. Navy was the first major military contract award for Booz Allen since Mr. Snowden revealed last month that he had used his job for the McLean, Va.-based company to take vast troves of classified government information…