The German picked up the problem while on international duty on Saturday.
Mancini was more optimistic about Micah Richards' injury, renewing hope that he may yet be fit to face Manchester United in the FA Cup semi-final.
The confirmation of the severity of Boateng's problem comes as a blow to City's hopes of finishing in the top four this season - and with it earning a place in the qualifying stages of the Champions League.
The Eastlands side are currently fourth in the Premier League, four points clear of Tottenham but having played a game more.
Mancini said: "He [Boateng] will have surgery in the next two or three days. Maybe he will be fit for the last two games [at home to Stoke on 14 May and away to Bolton on 22 May]".
The 22-year-old, signed from German club Hamburg prior to the 2010 World Cup, has made 24 appearances for City this season.
Mancini raised hopes that Richards could be fit to face Manchester United on 16 April, despite seemingly being ruled out.
Richards, 22, picked up a hamstring injury in England Under-21's 4-0 victory over Denmark on 24 March and was set to be out for four to six weeks.
Richards himself said on Tuesday: "All I can do now is concentrate on getting back as quickly as possible. I must admit I did think 'why me?' for a while when I heard the news [on missing the semi-final].
"Of all the games to miss, a Wembley date with United is the last one any player would choose. It is not what I wanted to hear. I felt sick when I was told."
However, Mancini said on Friday: "We are trying to get him fit for the semi-final. I don't know if it is possible but we hope."
Pablo Zabaleta is available for Sunday's match at home to Sunderland, having returned from Argentina where he was on compassionate leave to visit his sick father.
Now, everything Mario does is big news. I have spoken to him. I hope he can change his behaviour
Roberto Mancini
Blues boss Mancini also claimed he has no regrets over the signing of controversial striker Mario Balotelli, but did state he wants to see an improvement in the striker's conduct.
The Italian international, signed from Inter Milan for ?24 million, has been in the headlines for his off-field behaviour more than his contribution on the pitch.
"I do not regret signing him," said Mancini. "Mario is a fantastic player. He is a 20-year-old, so it is usual his behaviour is not good enough.
"I understand this situation very well. Playing here could be a fantastic experience for him. He has started 15 games and scored 10 goals. But he has to improve his behaviour.
"Now, everything Mario does is big news. I have spoken to him. What I said will remain private but I hope he can change his behaviour," Mancini added.
Source: BBC Sport
Source: BBC Sport