The world’s biggest makers of shampoo, detergent and packaged food will test selling their products in reusable containers, adopting a milkman-style model to address mounting concerns about plastic waste.

Procter & Gamble Co., Nestlé SA, PepsiCo Inc. and Unilever PLC are among 25 companies that, this summer, will start selling some products in glass, steel and other containers designed to be returned, cleaned and refilled.

Critics...