Guardiola said on Tuesday: “He [Stones] is out four, five or six weeks. He was injured in training this morning. It is a muscular problem.”
Stones’ absence will add to the defensive problems for City boss Guardiola, with French centre-back Aymeric Laporte already likely to be ruled out until January.
0:37 Pep Guardiola played down any fears over City's defensive crisis
This leaves City with just one recognised first-team centre-back going into Wednesday’s fixture against Shakhtar, with 18-year-old Eric Garcia or central midfielder Fernandinho in line to partner Nicolas Otamendi.
Guardiola added: “For me as a manager it is an incredible challenge. But I believe in something people don’t know about – spirit and commitment. We will make steps forward to solve this problem.”
Stones started alongside Otamendi in central defence against Norwich and the pair were often caught out of position as the Canaries’ forwards scored three times, but Guardiola has backed his defenders.
5:04 Jamie Carragher and Gary Neville analyse City’s centre-back partnership of Nicolas Otamendi and Stones and why it will cost them the Premier League title
He added: “I have a lot of respect for what John and Nico have done. Football is not about how you handle the good situations. It is about how you handle the bad ones.”
Phil Foden has not travelled with the rest of the City squad to Ukraine due to illness, but Guardiola revealed he could be back in time for Saturday’s Premier League fixture at home to Watford.
Analysis: What does Guardiola do now?
Sky Sports’ Jack Wilkinson:
“Vincent Kompany’s departure in the summer was already a sizeable obstacle for City to overcome in isolation. But the loss of Stones on top of Aymeric Laporte’s six-month injury lay-off has presented the Manchester City boss with a defensive crisis that needs solving fast.