The U.S. has raised the stakes in a battle with Beijing over intellectual property by restricting American firms from doing business with a state-owned Chinese chip maker that Micron Technology Inc. has accused of stealing its secrets.

Citing national and economic security concerns, the Commerce Department said Monday that it will begin restricting American companies from selling software and technology goods to Fujian Jinhua Integrated Circuit Co., a semiconductor startup into which the Chinese government has been pouring...