WASHINGTON—The Trump administration is moving to curb the sale of imported counterfeit goods over the internet, warning electronic commerce platforms and warehouse operators of greater scrutiny and penalties if they don’t help ferret out fakes.

The Department of Homeland Security is set to release a report Friday outlining its immediate actions and longer-term goals for enlisting e-commerce players to combat counterfeit products that officials say undermine U.S. technology and manufacturing, harm bricks-and-mortar retailers...