The Justice Department’s intervention in the Federal Trade Commission’s case against chipmaker Qualcomm Inc. is an unusual move that could widen the rift between the government’s federal antitrust enforcers.

In a late night filing May 2, the DOJ urged U.S. District Court Judge Lucy Koh to avoid any drastic penalty against the San Diego-based company as it could stall innovation and hamper efforts to commercialize 5G, the next generation of wireless technologies. The DOJ asked for an evidentiary hearing if...