Bardsley had been named as one of two goalkeepers in Hege Riise’s 18-player squad for the Olympic Games in Tokyo.
A decision on her replacement will be announced in due course, with the competition running from 21 July to 6 August.
Bardsley, currently on loan at US side OL Reign, was hurt in the closing stages of a fixture with Washington Spirit last month.
The two-time World Cup semi-finalist with England was also part of the 2012 London Olympics squad and is regarded as one of the most experienced shot-stoppers in the game.
It’s a huge blow for Bardsley, who has been at City since 2014.
She said: “After a difficult road back to fitness and form, being selected for Tokyo felt like the greatest achievement.
“Then, to be forced to withdraw through injury so close to the Games feels devastatingly cruel. Regardless of the situation, I’ll do whatever I can to help my teammates and Team GB every step along the way. I wish nothing but success for everyone.”
GB Football head coach Hege Riise added: “Losing Karen is a big blow for us – but more importantly for her. She has been an incredible international goalkeeper for many years and her presence in the squad would have also helped the younger players in the group.
“Of course, this is football and this means an opportunity for someone else to take. The group are very positive about the challenge ahead and can’t wait to get started.”
Everyone at City wishes KB a swift return from injury.