She has not played since her victory at January's Australian Open which brought a 23rd Grand Slam singles title and saw her return to the top of the rankings.
However willam had a problem with her left knee was of more advantage to her opponent and will sideline the 35-year-old for Indian Wells and the subsequent WTA Tour event in Miami.
"Sadly, I have to withdraw from the BNP Paribas Open in Indian Wells and the Miami Open," she said.
"I have not been able to train due to my knees and am disappointed I cannot be there. I will keep moving forward and continue to be positive. I look forward to being back as soon as I can."
Angelique Kerber will now reclaim the No 1 spot from Williams, who needed to reach the semi-finals in Indian Wells to retain her position.