The Food and Drug Administration plans to ban the sale of fruity flavors in cartridge-based e-cigarettes, but the restriction won’t apply to tank vaping systems commonly found at vape shops, according to people familiar with the matter.

The action is seen as a compromise between Trump administration officials who want to address a rise in teen vaping and those concerned about the impact on small businesses and the possible political fallout for President Trump, these people said. Polls commissioned by the vaping industry have...