Altria MO -0.16% Group Inc. is in talks to take a significant minority stake in e-cigarette startup Juul Labs Inc., according to people familiar with the matter, a move that could give the Marlboro maker greater access to a rapidly growing but increasingly controversial segment of the nicotine market.

No deal is imminent, the people said, but should there be one it would be big: Closely held Juul, a three-year-old company based in San Francisco with more than 1,000 employees, was valued at $16 billion in a funding round this summer.

Juul’s rapid growth—it had $1.8 billion in retail sales in the year ended Nov. 17, according to Nielsen data cited by Wells Fargo—has made it one of the most valuable U.S. startups, but it has drawn criticism because of its products’ popularity with teens.

A tie-up would represent a major reordering of the cigarette industry, which is being roiled by technological innovation and new government regulations.

Any deal is likely several weeks away, one of the people said, and there might not be one at all.

Juul is the dominant e-cigarette player with vaporizers resembling USB sticks and refill pods containing nicotine-laced liquid. Its sweet flavors, including mango and cucumber, are popular with middle-school and high-school students.

The company says it is targeting adult smokers, which threatens Altria’s lucrative but shrinking cigarette business. Nearly 38 million, or 15.5%, of American adults smoked traditional cigarettes in 2016, down from 20.9% in 2005, according to the Centers for Disease Control and Prevention.

Altria’s stock had declined nearly 20% over the past year as the company grappled with declines in traditional smokers and a potential U.S. ban on menthol cigarettes. It still has a market value of more than $100 billion.

Altria also sells e-cigarettes, but Juul has leapfrogged it and traditional rivals like British American Tobacco PLC, which makes Camel and Newport cigarettes, in the roughly $2.8 billion U.S. e-cigarette retail market.

Juul, whose products are sold online and in convenience stores, gas stations and vape shops, accounted for about three-quarters of the U.S. e-cigarette market in the four-week period ended Nov. 17, according to the Wells Fargo analysis of Nielsen data. Altria represented just 4.3% of the market in the same period.

Linking up with Altria could enable Juul to benefit from the shelf space Altria has carved out in stores for brands like Marlboro, Parliament and Skoal, and give the startup access to the legions of cigarette smokers the big tobacco company enjoys.

More broadly, it would help Altria defend itself against inroads from e-cigarettes, and expand the Richmond, Va., company’s business beyond the U.S. Juul products are sold in Canada, the U.K., Israel and Russia and the company has expansion plans in Europe and Asia.

But a deal would likely come at a steep price given Juul’s lofty valuation, especially in light of threats the startup faces from regulators. Details of the discussions, including how they might value Juul, couldn’t be learned.

Juul has come under attack from groups and elected officials who blame its devices for a rise in teenage vaping. The number of U.S. high-school students who used e-cigarettes rose 78% between the spring of 2017 and this past spring to 3.05 million, according to data from the National Youth Tobacco Survey.

This month, in a major potential blow to Juul, the Food and Drug Administration announced plans to place sharp restrictions on sales of flavored e-cigarettes, effectively pulling sweet and fruity flavors from convenience stores and gas stations.

Juul recently said it would stop selling most of its flavored liquids at bricks-and-mortar stores. The company will continue to sell all its products on its website, which Juul says has age-verification tools. The company also has discontinued its Facebook and Instagram social-media accounts, which had helped fuel its rapid growth.

Altria said in October it was pulling its pod-style e-cigarettes from the market and discontinuing the sale of many flavors after the FDA asked manufacturers to submit proposals to curb a surge in underage use.

Altria’s stock has fallen sharply since the FDA announced earlier this month that in addition to restricting e-cigarette sales it would seek a ban on menthol cigarettes. Menthols represent about 20% of Altria’s cigarette volumes. Such a ban would take years to implement.

Early Juul investors included a family office founded by Nicholas Pritzker, a billionaire whose family wealth is tied to the Hyatt Hotels empire. In the summer, investment firm Tiger Global Management invested $600 million in Juul as part of a funding round that raised more than $1 billion.

Write to Dana Mattioli at dana.mattioli@wsj.com and Jennifer Maloney at jennifer.maloney@wsj.com