The central defender was substituted midway through the first half at the King Power stadium after pulling up clutching his leg.
"John Stones, we are going to miss him for a long time, maybe six weeks off," said Guardiola after the game.
The 23-year-old has been one of City's standout players this season, also establishing himself as one of England's premier central defenders in the lead-up to the World Cup.
Guardiola cited his two recent appearances for England as a contributory factor in the injury.
"He was in a good, good condition. He was perfect leading the back four and has the personality to play not only with the ball but also without it.
"But that has happened with this amazing FIFA and UEFA calendar – at the end the players go down.
"You play 90 minutes, 90 minutes, 90 minutes and then go to your international team and play two 90 minutes that don't count for anything in terms of points.
"At the end, these kind of things happen. That's why I will rotate the team because, if not, many players will go out."
City face a logjam of 13 fixtures into the new year -- just over one game every three days -- as they seek to consolidate their lead in the Premier League, reach the League Cup semi-finals and complete their Champions League group games.
"It is tough because the calendar is so demanding," said Guardiola. "We don't have many central defenders and they will suffer but we will find a solution."
That is likely to revolve around Vincent Kompany, who started Saturday's game alongside Stones in central defence after more than two months out with a calf injury.
Kompany completed 90 minutes, although was fortunate to escape an early red card after scything down Jamie Vardy after three minutes.
That moment aside, Guardiola was delighted with his captain's return and said he is looking for the 31-year-old Belgian to stay fit after years blighted by injury.
"I am really impressed because after more than two months injured and (having had) one game at international against Gibraltar and to play at that level shows how strong he is in his mind," said Guardiola.
"At the last part of last season he came in and helped us a lot. Vince is a little mystery and hopefully he can be fit for the coming games."
Stones's absence will be further cushioned by the return from suspension of another central defender Nicolas Otamendi against Feyenoord on Tuesday, a game City will be keen to win in order to qualify as Group F winners ahead of the Champions League knockout draw.
(Reporting by Neil Robinson; Editing by Christian Radnedge/Rex Gowar)
