The clash between the division's two top-scoring sides provided plenty of entertaining moments but keepers Kasper Schmeichel and Joe Hart were equal to everything thrown at them at the King Power Stadium.
Jamie Vardy, the league's joint leading scorer with 15 goals alongside Romelu Lukaku of Everton, wasted Leicester's best chance late in the first half.
Manchester City, who have not won away in the league since September, went close through Raheem Sterling and Nicolas Otamendi.
Hosts Leicester, who suffered their first defeat in 11 league games at Liverpool on Saturday, have 39 points from 19 games and trail Arsenal on goal difference.
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Manchester City, without defender Vincent Kompany who could be out for another three weeks with a calf problem, leapfrogged Tottenham Hotspur to go into third place. They trail the top two teams by three points.
Leicester manager Claudio Ranieri thought his side showed signs of fatigue at Anfield but was delighted with their effort on Tuesday, saying a point apiece was a fair result.
"I wanted to see a reaction from the Liverpool game and it was good," the Italian told reporters.
"We were calm, tried to do our job. We created chances but so did Manchester City. The draw is right."
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The visitors began the season with three successive away wins but have not returned home with three points since victory over Crystal Palace on Sept. 12.
Manchester City manager Manuel Pellegrini was buoyed by the clean sheet but, with striker Sergio Aguero needing "two or three more games" to return to top fitness after injury, expressed frustration that his side lacked a cutting edge.
"We came for three points, had more possession, more attempts, did more things to win the game," said Pellegrini.
"If you can't win it's important not to lose and we were solid against a difficult team. I'm not happy but not disappointed also because we played well."
Manchester City dictated for long periods of the first half with Sterling a constant menace.
Schmeichel made the first meaningful save from Kevin De Bruyne and then, following fine link-up play, kept out Sterling's strike before again denying the England international from the edge of the box.
Leicester finished the opening 45 minutes strongly. Marc Albrighton, sliding in at the far post, just failed to get on the end of a delightful low curling centre from Christian Fuchs that went across the face of the goal.
Vardy, isolated up front for long stretches, was then handed a great opportunity to score.
Fernandinho gave away possession just outside his own box and Vardy, played in behind the defence, blazed his shot over Hart's bar, hardly the finish of a striker high on confidence.
The second half was more even but neither side could find the elusive breakthrough.
Leicester's N'Golo Kante and Albrighton were off target, Fuchs tested Hart with a stinging shot while Manchester City's best effort after the break came from an Otamendi header thatSchmeichel turned around the post.
(Editing by Tony Jimenez)
