Detroit’s car companies are targeting May 18 to resume some production at their U.S. factories after the companies shut down their plants in March amid the spread of the coronavirus, according to people familiar with the plans.

Executives from General Motors Co., Ford Motor Co. and Fiat Chrysler Automobiles NV in recent days tentatively settled on the timeline after talks with United Auto Workers leaders and Michigan Gov. Gretchen Whitmer’s office, the people said.

The...