City skipper Kompany limped off in the sixth minute of the Champions League last-16 second leg at the Etihad Stadium, which ended 0-0 to see Pellegrini's side go through with a 3-1 triumph on aggregate.
And the manager said after the contest: "Vincent unfortunately again has a muscle injury in his calf, the same problem as he had before.
"We will know maybe tomorrow or the day after how important it is, but always a muscle injury is a minimum of one month."
He added: "Having this problem in his calf and it being the middle of March, at least three-quarters of the rest of the season he will not play.
"I think he must be very strong with his mentality.
"It is very difficult to accept it, but there is nothing he can do. So we must see tomorrow with the examinations."
Kompany has repeatedly suffered with calf problems this season and throughout his City career.
The Belgian was on Tuesday making only his seventh appearance since his last spell on the sidelines, and his sixth in a row, with all of them having been starts.
The first of those last six appearances was as recently as February 24, and Pellegrini was asked after Tuesday's match if he felt he had taken a risk with Kompany's fitness that had backfired.
hypervenom phantom ii grey uk The Chilean replied: "You always take a risk - the work during the week is also a risk. But he had recovered without any problem.
"It was the sixth game, but he had not felt any problems before the games, so I think it was not a risk and bad luck only."
adidas x 15.1 black uk A further worry for City ahead of Sunday's Barclays Premier League derby clash with Manchester United was another of their centre-halves, Nicolas Otamendi, hobbling off in the 23rd minute with what was subsequently confirmed to be a dead leg.
Pellegrini said of the Argentinian: "He has an important kick.
"I think that will just be a couple of days and he may recover - we will see the way it develops over the next days."
superfly mercurial black uk On the positive side, the result took City through to the quarter-finals of the Champions League for the first time.
magista obra black uk Pellegrini said: "I am happy with the achievement. It is important for the club to be improving every season.
"In the last two seasons we have been unlucky in the round of 16 - we were unlucky to play Barcelona. This year we have arrived and it is history.
"It was a tactical game, we didn't take any risks, just (played) to qualify and waited to see if they gave any space - but they played a quiet game."
Dynamo failed to make much of an impression and, injuries apart, City completed the job with little alarm.
elastico superfly black uk Nevertheless, visiting coach Sergei Rebrov was pleased with his side's efforts.
The former Tottenham and West Ham striker said: "We lost this game in Kiev, but I say thank you very much to the players.
"City have big players with big experience - but it is not easy now. I wish them well."
