WASHINGTON—The Federal Communications Commission is moving to place another restraint on the U.S. business of Huawei Technologies Co. and ZTE Corp. by banning U.S. companies receiving federal subsidies from purchasing the Chinese firms’ equipment.

FCC Chairman Ajit Pai set the proposal for vote at the agency’s meeting on Nov. 19. It would designate Huawei and ZTE as national security threats and tell U.S. firms not to buy their equipment using money from an $8.5 billion federal fund designed to expand telecommunications service...