Ogbonna was injured in the 3-2 victory over Liverpool two weeks ago and will require surgery.
“We think surgery will take place over the next couple of days and that is really sad, he has done a great job for us, he is a great boy, a great team player,” Moyes told reporters ahead of Saturday’s clash with Wolverhampton Wanderers.
“He is someone we love having around and more importantly his performances have been excellent for us so it is a real sad moment for him and us.”
Asked when Ogbonna could return, Moyes said: “Most people who know about injuries and cruciate ligament injuries know they tend to take somewhere around about nine months.
“You look at (Virgil) van Dijk and people of that ilk and how long it takes for recovery. There is not a quick return from cruciates, there is a period which has to be taken for recovery time. So I would probably say yes it will be hard for Angelo to play again this season.”
It is a blow for West Ham who have enjoyed a superb season so far, climbing to third in the Premier League and only three points behind leaders Chelsea.
“If the season finished now I would be ecstatic, drinking champagne because of how good the team has done but we have another 20 or more games to go so we just have to continue how we have been playing and keep the players pushing on,” he said.
“But I think we can play better, there is more to come and players who can step up again.”
He again played down West Ham as title challengers, but added: “But I want to challenge the top four.
“We finished two points outside last season but that is a good target to give the players.”
West Ham have been further boosted by investment into the club by Czech billionaire Daniel Kretinsky who earlier this month bought a 27 per cent stake in the London club.
“It’s great, we got a new coffee machine the other day!” Moyes joked. “I had a chance to meet Daniel after Liverpool he seems a very charming fellow and is a really good addition to the board and I am looking forward to working with him.
“It looks and feels like a good move for West Ham and we are looking forward to him having an impact and moving forward.”