Nike Inc. is yanking a U.S.A.-themed sneaker featuring an early American flag after NFL star-turned-activist Colin Kaepernick told the company it shouldn’t sell a shoe with a symbol that he and others consider offensive, according to people familiar with the matter.

The sneaker giant created the Air Max 1 USA in celebration of the July Fourth holiday, and it was slated to go on sale this week. The heel of the shoe featured a U.S. flag with 13 white stars in a circle, a design created during the American Revolution and commonly...