E-cigarette startup Juul Labs Inc., faced with a regulatory crackdown and criticism that its marketing has attracted underage users, plans to stop selling most of its flavored nicotine liquids at bricks-and-mortar stores, according to people familiar with the matter.

Juul plans to keep selling menthol- and tobacco-flavored products in stores, while all flavors, including cucumber and mango, will remain on its website, which has age-verification controls, the people said. The planned restrictions could heavily affect Juul...