The 36-year-old Manchester City player, one of two goalkeepers in Hege Riise's 18-player group for the Games, was hurt while playing on loan at OL Reign last month; a decision on her replacement will be announced in due course
"After a difficult road back to fitness and form, being selected for Tokyo felt like the greatest achievement, but to be forced to withdraw feels devastatingly cruel," she said.
"Then, to be forced to withdraw through injury so close to the Games feels devastatingly cruel.
Great Britain, who reached the quarter-finals at 2012, start their Tokyo campaign against Chile on Wednesday, 21 July, before further Group E games against hosts Japan and 2016 bronze medallists Canada.
"Regardless of the situation, I'll do whatever I can to help my team-mates and Team GB every step along the way. I wish nothing but success for everyone."
Team 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."
What do you have to say about this friends