American Apparel Inc.'s board moved Wednesday to fire founder and Chief Executive Dov Charney, citing an "ongoing investigation into alleged misconduct."

The move kicks off a fight at the top of the company, which is already struggling with poor results and debt. The board wouldn't specify the allegations but said it intends to fire Mr. Charney for cause once a 30-day period to resolve the conflict called for in the CEO's contract expires. The company said the move could leave it in default under its credit agreement,...