WASHINGTON—The Justice Department is moving to terminate legal rules that have governed the movie industry since the late 1940s, a step that could shake up how movies are distributed and the terms on which they hit the big screen.

The department’s antitrust division has determined that rules limiting film studios’ influence over theaters have outlived their usefulness in a movie business that has changed considerably since the curbs were first imposed. The rules set to be lifted were laid out in decades-old legal settlements...