Williams, now ranked at 23 in the world, has been hampered by back problems since the Australian Open.
The 32-year-old will be replaced in the tournament by Czech Republic's Andrea Hlavackova.
She also missed last week's Open GDF Suez tournament and will skip the upcoming Fed Cup match against Italy because of the setback.
The injury comes after an average start to the season for the seven-time grand slam champion which saw her suffer a heavy defeat to Maria Sharapova in the third round of the Australian Open.
Sister Serena Williams is set to play in Qatar along with world number one Victoria Azarenka.