The 22-year-old Brazilian played 72 minutes of the Dutch champions' incredible 4-4 Champions League draw at Chelsea on Tuesday, but could now be sidelined until next year.
"It's a big blow for him and for the team," said Ten Hag.
The winter break in the Netherlands starts on December 22.
Neres, who has scored six goals in the Dutch Eredivisie this season, will miss Ajax's crucial final Champions League group games against Lille and Valencia.
Ajax are six points clear at the top of the Eredivisie from AZ Alkmaar after going the opening 12 matches unbeaten.
But last season's surprise Champions League semi-finalists face a battle to reach the last 16 this year after blowing a 4-1 lead with nine men to draw with Chelsea, sitting level on points with both Frank Lampard's side and Valencia in Group H.
Neres netted 12 times in all competitions last season, including against both Juventus and Real Madrid.