Mattress Firm Inc., the largest specialty mattress seller in the U.S., filed for bankruptcy protection Friday, the victim of increasing competition from discount retailers, too many of its own stores and the loss of a key supplier.

The Houston-based retailer, which had gobbled up dozens of rivals over the past decade, sought chapter 11 protection in U.S. Bankruptcy Court in Wilmington, Del. The filing follows a deal struck in July with bondholders of its troubled parent, Steinhoff International Holdings NV, which took Mattress...