The head of the U.S. Food and Drug Administration said that a government shutdown prevents it from doing some routine food safety inspections, and that the agency is weeks away from running out of funds it uses to review new drugs and medical products.

“The functions that can most directly impact consumer safety will continue, to the best of our abilities, subject to the legal and financial limitations of the current circumstances,” FDA Commissioner Scott Gottlieb said in a tweet Jan. 8.

In a subsequent post Jan. 9, Gottlieb said the agency’s limited food safety inspections would be focused...