Kroger Co. said it would stop selling guns to buyers under 21 years old through its Fred Meyer locations, the third major retailer to tighten its policies while lawmakers continue to debate how to respond to the latest school shooting in America.

The U.S.’s largest supermarket chain said Thursday it would raise the minimum age to purchase arms and ammunition in all of its Fred Meyer stores in response to the Parkland, Fla., high-school tragedy. Kroger currently sells firearms at 43 Fred Meyer locations in Alaska, Idaho,...