The world number two and top seed - who beat Serena Williams in the final of WTA Doha on Sunday - said that she had been playing through the injury, but had reluctantly decided that she could not continue to do so.
"It happened last week. I have been obviously playing on it a lot, so going to a new tournament right is too much to handle right now," she said.
"It keeps getting worse. It was an unfortunate decision that I had to make, and obviously I'm very disappointed with that."
It is the second year running that the Belarus star has withdrawn from the tournament.
"We wish her a speedy recovery and look forward to seeing her back in Dubai next year," said tournament director Salah Tahlak.
Azarenka's place in the draw will be filled by lucky loser Carla Suarez Navarro.