Manager Manuel Pellegrini revealed that the Belgian centre-back faces another lengthy spell on the sidelines after limping off during the 4-1 Boxing Day win against Sunderland.
Kompany had made his comeback as a substitute against the Black Cats after six weeks out with another calf injury and he watched the draw with the Foxes from the stands at the King Power Stadium.
“Vincent has an injury, a second degree of his calf,” Pellegrini said.
“It`s not the same injury, the same calf but in a different part. I am not a doctor but normally a muscle injury of less than three or four weeks is very difficult, especially in the calf.
“We hope that he can recover as soon as he can but it`s very important until we solve this to defend the way we did in this game.”
Pellegrini`s side moved to within three points of leaders Arsenal with a point at Leicester while the home side went level on points with the Gunners at the season`s halfway point.
But Manchester City are now without a win in six away games in the Premier League – a record that has prevented them building fully on their flying start to the season.
They dominated long spells of the first half against Leicester but were unable to find a goal and found themselves forced back by the home side after the break.
Pellegrini said: “I don`t divide games that we play into home and away.
“We have a season and it`s important to have the amount of points you need to win the title.
“We need to win but we are the best team at home.
“In the second half of the season we will keep improving and if you ask me if I`m happy, I say yes because we are near the top of the table.
“We had more possession and attempts than Leicester and did more to win the game, but if you can`t win it`s important not to lose.
“We were very solid and defended well against a difficult team.
“I`m not happy but I`m not disappointed either because we played well but didn`t score.”Leicester will end 2015 with a share of the Premier League lead after entering the year at the bottom of the table.
They are just one point away from manager Claudio Ranieri`s initial target of 40 points with their supporters beginning to dream of a genuine title challenge.
The Italian said: “What we are doing is unbelievable. The first half of the season is magnificent and I don`t have words to say how happy I am.
“The Premier League this season is strange.
“The bigger teams should be able to stay away from us but we are there and we would love to stay there.
“I know it`s not our position but we will fight for it.
“We`re the basement and the other teams are a villa with a swimming pool. It`s not easy for us but we want to fight with everybody.
“It`s a miracle what we`re doing. I`d love this to continue but it`s not easy. I can only say well done to our players and our fans are unbelievable, they support us and they push us.”
“2015 was fantastic for Leicester and I hope 2016 can be better.”