Kompany has missed more than half of City's league games this season, playing in nine out of the 19, and hobbled off within 10 minutes of appearing as a second half substitute against Sunderland.
He had not played a game since the trip to Aston Villa in early November in what was City's last clean sheet.
"Vincent has an injury, second degree on his calf so we'll see how many weeks he will be out," Pellegrini told reporters after the Leicester game. "I do not think it will be less than three-four weeks.
"I am not a doctor, but with a muscle injury, it will be very difficult for him to be back in less than four weeks.
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"But without him, we must continue to defend as did tonight. We did more than Leicester to win the game."
Manchester City begin the new year with games against eight place Watford in the league, followed by trips to Everton for a League Cup match and to Norwich in the FA Cup - all within a week.
(Reporting by Nayan Das in Bengaluru; editing by Amlan Chakraborty)
