The 22-year-old has featured 20 times for the Dutch champion in all competitions this season, scoring six times and providing a couple of assists.
Neres played 72 minutes of Ajax's 4-4 UEFA Champions League draw with Chelsea at Stamford Bridge on Wednesday (AEDT), but he damaged his meniscus in the first half and is sidelined until 2020.
"We will have to make do without David until the winter break," Ten Hag said ahead of Monday's (AEDT) home 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, who has started four games for Brazil this year, will miss Ajax's crucial UEFA Champions League games with Lille and Valencia.
"It's a major setback. These things happen. I feel really sorry for him," Ten Hag said.
"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 a better shape. That makes it a big blow for the entire team as well."
Eredivisie leader Ajax is top of UEFA Champions League Group H, level on points with Chelsea and LaLiga club Valencia.