Williams, 32, once the world's top-ranked player, also is skipping this week's USA-Italy Fed Cup match-up because of the injury.
Williams lost to Maria Sharapova in straight sets in the third round at the Australian Open last month.
The Qatar event will feature current world No. 1 and reigning champion Victoria Azarenka and Williams' younger sister Serena.
Notable deaths of 2014 [PHOTOS]