Stones suffered the ailment during Tuesday's training session. He had just returned from a thigh injury over the weekend, suiting up for City's stunning 3-2 loss to newly promoted Norwich City.
Nicolas Otamendi is the team's only natural center-back remaining, leaving Guardiola to consider moving defensive midfielder Fernandinho into the heart of City's defense. The gaffer also hopes Eric Garcia (18) and Taylor Harwood-Bellis (17) can establish themselves in the coming months.
"What we will not do is complain that they are not able to play," he said.
Guardiola added: "Football is not how you handle good situations, but how you handle bad ones. We won seven titles and no one gave us anything, we did it ourselves. I am ready for the challenge. I like this situation."
City will kick off their Champions League campaign Wednesday when they visit Shakhtar Donetsk.