The 23-year-old has featured in every Premier League game for City so far this term but was forced off just 28 minutes into his side's 2-0 victory at Leicester City today clutching his leg.
Speaking to press after the game, Guardiola confirmed that Stones's injury could see him miss crucial clashes with title rivals Manchester United and Tottenham Hotspur over the next month.
"It is unfortunate for us and for John and I think he might be out for six weeks with that type of injury," he told reporters.
"We don't have a lot of central defenders. But the spirit in the team and with all the players is good so we are going to find a solution."
Stones had already featured 18 times and scored three goals for City in all competitions this season, helping them to a healthy lead at the top of the Premier League table.