The 27-year-old, who broke her thumb at London 2012, had recently recovered from a fractured wrist and shoulder reconstruction surgery.
Gibbons returned to claim silver for England in the 78kg category at the Commonwealth Games in July.
"No athlete gets to the top without their share of injuries, hopefully this will be my last one," Gibbons said.
Gibbons, who suffered the ankle ligament injury in training, has her long-term sights set on the Rio Olympics in 2016.
She said: "I know that when I am my best I can be one of the best in the world, so I will just have to keep doing the rehab to get back as soon as possible."
Britain will send a four-strong team out to Russia for the world championships, held from 25-31 August, including Commonwealth Games gold medallists Colin Oates, Ashley McKenzie and Natalie Powell as well as Sally Conway, winner of bronze in Glasgow.