Add J.C. Penney Co. to the growing list of American retailers that will shrink to survive a shift away from traditional stores.

The 114-year-old chain, which had avoided mass closings despite years of losses, said it would shut as many as 140 of its roughly 1,000 stores by June. The company said it was also offering a voluntary buyout program to 6,000 of its employees.

Penney...