Ndidi has been operating as a makeshift central defender, but suffered an abductor injury in the Premier League win over Burnley which will need surgery.
Rodgers saw his side beaten at home in the Carabao Cup by Arsenal on Wednesday night, when the Foxes boss named a completely fresh XI as James Maddison was handed his first start of the campaign.
The Northern Ireland defender has now served a suspension following his sending-off against Manchester United at the end of last season and recovered from a thigh strain picked up while on international duty.
Rodgers feels Leicester can regroup as they look to maintain a perfect start to the new Premier League campaign.
Confirming the need for Nigeria international Ndidi to have an operation, Rodgers said: "That will probably take place tomorrow morning. It's unfortunate.
"It has come right off the bone, so he is going to be (out) up to 12 weeks we think.
"Towards the end of last season, he felt some pain there and he felt it late and felt it during the Burnley game, but he carried on with his amazing spirit.
"But when we got the scan after the game, it did not show up so well.
"It is unfortunate. I am sure he will make a good recovery, but there is no doubt he will be a miss."
Rodgers maintains Leicester have options to fill in and do not need to buy a ready-made midfield replacement in the closing days of the transfer window.
"We have other priorities with whatever resources we have, we probably are looking at other positions to use that," he said. "We have players that are capable of stepping in.
"Nampalys Mendy has started the season very well, Hamza Choudhury was excellent against Arsenal, really covered the ground and defensively was very good.
"We have enough cover at this moment in that position."
Evans is expected to be involved again alongside Caglar Soyuncu on Sunday.
"He is fine," said Rodgers. "He has been training over these past number of days so he is available.
"He has had a good couple of weeks and I think for most players, they are not going to be at 100 per cent, but I would still have at Jonny Evans at 80 per cent because he is such a top player."
Rodgers is expecting a testing encounter against City on Sunday.
"It is another good measure for us," he said. "We know realistically where we are at, but the challenge is for us to be competitive.
"They have world-class players and a world-class manager, and that makes it very tough."
Winger Cengiz Under has been signed on a season-long loan from Roma, but will not be in the squad for Sunday as the club waits for international clearance to be completed.
Ricardo Pereira is stepping up his recovery from a serious knee injury and remains around a month away from contention.
Fousseni Diabate, meanwhile, has moved to Turkish side Trabzonspor on a permanent deal.