The 22-year-old picked up the knock during the 4-4 thriller st Stamford Bridge on Tuesday, and tests have since revealed that he has damaged the meniscus cartilage in his knee.
He played 72 minutes of the clash in west London before being replaced by Perr Schuurs, and Ten Hag has revealed the injury is worse than initially thought.
"We will have to make do without David until the winter break," the Ajax boss said at his pre-match press conference ahead of Sunday's Eredivisie meeting with Utrecht.
"At half-time [against Chelsea] I asked everybody if they were okay and everybody said yes. Directly after the game, it was clear that he was injured, but we didn't expect that it was so heavy.
"I think it happened in the first half. There were two small moments when he got a knock. But I can't know for sure."
Neres has been linked with a move to the Premier League in the past, and former Brazil team-mate Richarlison has tried to get him to join him at Everton.
"Of course the Premier League interests me,” Neres said in the summer. “It's the best league in the world, and I've always wanted to play there. But I leave all that in God's hands.”
Neres has six goals in 12 Eredivisie games this season, and he’ll be a big miss for the club as they look to progress from Champions League Group G, and look to replicate last season’s success in the tournament in which they reached the semi-finals.
"It's a major setback,” added Ten Hag. “These things happen. I feel really sorry for him.
"It's a major blow for him, but for the team as well. But it's mainly hard for him, because he was getting in better shape. That makes it a big blow for the entire team as well."
Ajax top the both the Eredivisie and their Champions League group, but their game against Valencia in December will likely decide which of the two sides qualifies for the knockout stages.