The Argentina right-back, who has not yet featured this season after returning late following summer international duty, was hurt in training this week.
Pellegrini, speaking at a press conference to preview Sunday's Barclays Premier League trip to Everton, said: "Pablo Zabaleta yesterday had a problem in his knee with his ligaments so he will be out for around one month."
On the positive side, new midfield signing Fabian Delph is now back in training after suffering a hamstring injury during pre-season, as is fellow midfielder Fernando after a groin problem.
City brought in another new player this week as they signed Argentina centre-back Nicolas Otamendi from Valencia in a deal believed to be worth around £32million.
That move from City came despite a positive start to the new campaign in which they have beaten both West Brom and, most notably, champions Chelsea 3-0.
But Pellegrini says it was important to bolster the central defensive ranks with captain Vincent Kompany, Eliaquim Mangala and Martin Demichelis likely to face a heavy workload this season.
He said: "I think that we needed a centre-back
We analysed different options and we decided that Nicolas Otamendi was the best option
I think he is a very good player, he is improving.
"I know him from when he played in Porto with Mangala, both of them against Malaga in the Champions League
Last season with Valencia he had a very good season."
Despite that, Pellegrini is likely to keep Otamendi, 27, waiting for his full debut after two impressive displays from Kompany and Mangala.
He said: "In this moment, in the way we are playing, it is impossible to move Kompany and Mangala from their positions and all the rest of the players
They are in a good moment
We did not concede one goal in the last two games
We continue playing with the same."
The other centre-back in the City first-team squad, 20-year-old Belgium international Jason Denayer, may now find opportunities limited and could move out on loan for a second successive season after spending last year at Celtic.
Pellegrini said: "We will see will see now where he will go or if he stays here
We will decide in the next weeks."
City continue to be heavily linked with Wolfsburg playmaker Kevin de Bruyne, as they have been for most of the summer, but Pellegrini will not acknowledge any interest.
"I don't talk about rumours," he said
"I have to talk about so many players it is impossible
When things are finished, then I can talk about them."
City reportedly made a £47million offer for the former Chelsea player last week but there have been no developments since.
Pellegrini, however, has not ruled out further additions.
He said: "The window closes on September 1
Before that nobody knows what happens."
City can equal a club record of nine successive league wins if they maintain their strong start to the season with victory at Goodison Park this weekend.
Source : PA
Source: PA