WASHINGTON—The Justice Department is scooping up data from thousands of mobile phones through devices deployed on airplanes that mimic cellphone towers, a high-tech hunt for criminal suspects that is snagging a large number of innocent Americans, according to people familiar with the operations.

The U.S. Marshals Service program, which became fully functional around 2007, operates Cessna aircraft from at least five metropolitan-area airports, with a flying range covering most of the U.S. population, according to people familiar...