The Switzerland international requires surgery after being forced off at half-time in City's Champions League loss to Real Madrid at the Etihad Stadium on Tuesday.
Guardiola said at a press conference on Friday he expected the 29-year-old to be out for "eight to 10 weeks", which would mean him missing most of the rest of the season.
It is the latest in a series of injury problems to have hit City during what has been an underwhelming campaign and Guardiola suggested Akanji's willingness to play when not fully fit had cost him.
The City boss said: "Surgery on Saturday - his abductor is 'broken'.
"We wish the best recovery for Manu - speedy - because the effort he has done this season has been unbelievable.
"He and Nathan (Ake) have played in difficult conditions, not being on top, to help the team in emergency conditions due to the lack of players in those positions. In the end, the body said, 'enough is enough'."
Midfielder Jack Grealish lasted only half an hour against Real and is now rated doubtful for the champions' Premier League clash with Newcastle on Saturday.
Guardiola said: "It's not as tough as what Manu has done but I don't know if he will be ready for tomorrow. I don't think so, but we will assess in the next hours."
This weekend's game between two rivals for top-four places comes at an awkward time for City between the two legs of their play-off tie against Real, the first of which they agonisingly lost 3-2.
They now face a monumental challenge to turn things around at the Bernabeu and reach the last 16 and Guardiola hopes a good performance against Newcastle can change the mood.
He said: "When you are in the position we are in, the good results help a lot for the next games. Every time we get a result, the mood is better for everyone."
Yet with City and Newcastle level on points in fifth and sixth respectively, Guardiola is not expecting anything to be straightforward, saying: "Newcastle will be a contender for the top four or top five until the end."
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