The Federal Trade Commission is investigating whether e-cigarette startup Juul Labs Inc. used influencers and other marketing to appeal to minors, according to people familiar with the matter, ratcheting up pressure on a company whose products are blamed for a rise in vaping among teens.

The probe, which hasn’t previously been disclosed, began before the agency’s antitrust review of a December deal in which tobacco giant Altria Group Inc. invested $12.8 billion to take a 35% stake in Juul, those and other people familiar with...