It is unclear if the image was mistaken for fireworks or clouds.
In its apology, the company said it was an honest mistake by the social media manager, who was born after the 1986 explosion that killed all seven crew members, including schoolteacher Christa McAuliffe.
"We sincerely regret the insensitivity of that selection and the post has been deleted," the company said.
American Apparel has been the focus of media attention in recent weeks after the board voted to replace Dov Charney as chairman and announced its intention to remove him as president and chief executive "for cause," according to the company. Charney has been dogged by lawsuits and allegations of misconduct for years.