Blues captan Cahill has been a key player for the reigning Premier League champions this term, and his injury could force the club to look for a new centre-back in the January transfer window.
Chelsea manager Antonio Conte turned towards youngster Christensen as a replacement for Gary Cahill instead of the fit-again David Luiz who was named on the bench for the London side. Jamie Vardy was brighter than Alvaro Morata, Riyad Mahrez more unsafe than Eden Hazard.
Jan 6: Mourinho acknowledged he made mistakes but declared that he would never be banned for matchfixing.
The Blues were doing little in capitalising on the numerical advantage with 10 minutes to play while the visitors were organised at the back.
The Chelsea manager was heavily criticised by his own fans for substituting Eden Hazard for the tenth time this season and his gamble failed to pay off as replacements Willian and Pedro were unable to engineer a breakthrough. There were logical reasons for the change: get Hazard closer to goal and incorporate Cesc Fabregas into the side without losing midfield balance. Bakayoko is certainly a box-to-box midfielder, but his ability when he reaches either box is highly questionable.
But Chelsea soon showed signs of getting to grips with the game, Alvaro Morata pulling a save from Schmeichel after charging in along the byline, while the Dane did well to tip a fierce Fabregas drive over three minutes before half-time. He lacked the decisive touch in the final third of the pitch though.
Dragovic struggled to find his feet initially as he was troubled by Morata in the first-half but steadied as the game progressed.
Currently, Chelsea rely heavily on one system to beat teams - their 3-5-2.
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However, their comments have acquired more bite lately, beginning when Mourinho implied that Conte was a "clown" for his dramatic touchline celebrations, although he later claimed he was not referring specifically to the Italian.
Chelsea really need to rediscover their spark against Leicester, with Morata especially in need of a boost.
He feels Conte should have tried hard to keep the two key players, who were instrumental in Chelsea winning two out of the last three Premier League titles.
It made for tense viewing for the Chelsea home support.
The centre-back pulled up just 30 minutes into the game at Stamford Bridge as he chased Leicester striker Jamie Vardy and was given treatement on the field before limping off. But the Foxes were more proactive and dominated possession in the opening stages very impressively.
Chelsea are unbeaten in six league matches home and away, earning 14 points out of a possible 18.
Leicester continued to pose problems, with Riyad Mahrez beating Antonio Rudiger and crossing for Vardy, who could not connect at the far post.
The Algeria worldwide has rightly been criticised for being inconsistent since Leicester's title-winning campaign of two years ago, sometimes seemingly picking and choosing which matches he wants to dominate.
Chelsea pushed for a late victor but Tiemoue Bakayoko's poor effort flew over the bar before Schmeichel clawed Marcos Alonso's cross away from danger in stoppage time as the Blues wasted the chance to go second. He was fortunate to escape without a booking for diving.