In recent weeks, public health agencies have reported a number of serious illnesses believed to be tied to vaping, including a death in Illinois, raising questions about the products’ safety at any age. This week, Oregon heath officials said they were investigating the death of another person, who had used a vaping device containing cannabis. The health department in Milwaukee and the Illinois attorney general have issued statements urging people not to use e-cigarettes. This year, San Francisco became the first American city to ban the sale of the products.

[Read more about the mysterious vaping illness that is becoming an epidemic.]

In Michigan, Ms. Whitmer’s order would ban the sale of flavored nicotine vaping products in stores and online. She also instructed state health officials to stop any advertising or marketing of the products that uses terms like “clean,” “safe” or “healthy.” Tiffany Brown, a spokeswoman for Ms. Whitmer, said the new rules would be put in place in the next few weeks, and that businesses would then have a month to comply.

Because the rules had not been finalized, Ms. Brown said she could not answer questions about what penalties companies that violate the restrictions would face or how the online sales ban would be enforced. She said Ms. Whitmer’s administration was allowed to ban the products without legislative action because state laws allow such orders to protect public health and to respond to a health emergency.

Tony Abboud, the executive director of the Vapor Technology Association, an industry group, criticized the ban in a statement. He predicted that it would hurt small businesses in Michigan and create a black market for flavored e-cigarettes.

“The governor’s edict is not based on science or common sense,” Mr. Abboud said.

A statement from Juul Labs, one of the leading e-cigarette companies, said it favored a ban on flavors “that mimic candies or children’s foods,” but believed menthol-flavored e-cigarettes should be allowed.