Azarenka, 26, was seeded sixth for the tournament which begins on Monday.
The two-time Wimbledon semi-finalist has not played since retiring from her first-round match against Italian Karin Knapp at last month's French Open.
The Belarusian's withdrawal means five-time champion Venus Williams will move up into the top eight seeds.
It also means Britain's number one Johanna Konta moves up to 16th seed - meaning she will not face a higher-seeded player until round four, should she progress.
Azarenka, who won the Australian Open in 2012 and 2013, has been plagued by foot injuries in recent years.
She won bronze in the women's singles and gold in the mixed doubles at the London 2012 Olympics and her withdrawal comes just six weeks before the start of Rio 2016.
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Two-time Grand Slam champion Victoria Azarenka has been ruled out of Wimbledon with a knee injury, the tournament organisers have announced.