It is the first legal test of the eight-year-old law. The law requires companies to prominently notify app users about what identifiable information is being collected and how it will be used. California is the only state with an apps-privacy law.
Attorney General Kamala Harris filed the suit in San Francisco Superior Court.
Harris says the company missed a 30-day window to comply with the privacy law on its "Fly Delta" app, which is designed for use on smartphones and other mobile devices. Customers can log on to check in for a flight, review reservations, book flights and pay for checked baggage.
Delta had no comment on the pending litigation.
The Associated Press contributed to this report.