Johnson sustained the injury in an accident in training on Thursday and City initially ruled him out of Saturday's FA Cup tie against Notts County.
However, following the 1-1 draw against the League One side, Mancini revealed the bad news for City supporters.
"We have lost Adam Johnson for three months,'' Mancini said. "This will be a very big problem because he is an important player.
"The injury is like the one Aleksandar Kolarov had earlier this season. We do not have another player like Adam.''
The news means it is very unlikely that Shaun Wright-Phillips will be allowed to leave City prior to the close of the transfer window on Monday night, despite suggestions he will hand in a transfer request.
"I can understand his position," Mancini said. "We haven't had any offers for Wright-Phillips at this moment but it is difficult for Shaun to join another team now. We still have another 24 hours, so anything can happen but it probably affects it."
Tevez should be back for Wednesday's trip to Birmingham, part of a glut of fixtures that mean City will not play their FA Cup replay until the weekend of the fifth round in three weeks' time after snatching a late equaliser at Notts County this afternoon.
Neal Bishop nodded the hosts in front after an hour and for a while it looked as though the world's oldest Football League club would claim the scalp of the country's most expensive team.
"We didn't deserve to lose but this is the FA Cup,'' Mancini said. "We didn't want a replay before the game but I am happy to have one now.''
Paul Ince was full of praise for his players afterwards and insisted they deserve credit for their enterprising performance.
"I know how these games work,'' said the former England skipper. "You are playing a lesser team and you think you can cruise through. I did it with Manchester United. It is not the case. Belief can overcome complacency.
"On days like this, the club from the lower echelons should be given the credit they deserve not have people say City did not play well. We stopped them playing. It just felt like the clock stopped after we scored.''
It means another money-spinning trip to Premier League opposition for County, who defeated Sunderland at the Stadium of Light in the last round.
"We earned a few quid at Sunderland. Now we will get a few more at Manchester City,'' said Ince.
And Mancini might need to watch out after ordering special red wine from his old adversary, then not turning up to drink it.
"Brian Kidd and David Platt came in and I have known them both for a long time, so that was nice, but I didn't see Roberto,'' laughed Ince. "He told me to make sure I got some nice red wine too. I will pour it over his head when I see him.''
Meanwhile, City are to send a formal letter of complaint to Notts County after a senior official was denied access to the area around the dressing rooms at Meadow Lane.
Vicky Kloss, City's director of communications, was attempting to make contact with manager Roberto Mancini ahead of his TV interviews before the FA Cup tie when she was told by a steward she would not be allowed into the players' tunnel.
City claimed she was told she was being denied entry because she is a woman, which Notts County deny.
More angry words were exchanged after the 1-1 draw.
The episode came just eight days after Richard Keys and Andy Gray engaged in their infamous criticism of assistant referee Sian Massey at Molineux.
Notts County denied the claims from City, insisting Kloss was not prevented from entering the area because of her gender, but because she did not have the right pass.
A County spokesman said: "It's nothing to do with her being a woman. She was trying to get into an area without the correct accreditation.''
However, it has been established that Kloss' junior colleague, who is male, had been allowed to enter the same area five minutes earlier without being asked for a pass, which he did not have anyway.
City are so incensed about the manner in which their staff were treated that they intend to write to County chief executive Jim Rodwell for an explanation.