The 29-year-old former Real Madrid star left the pitch in tears with a leg injury during United's 1-1 draw against Chelsea last Saturday.
"Varane isn't in the squad," said Ten Hag at a press conference on the eve of United's Europa League match with Moldovan side Sheriff Tiraspol.
"He will be out until the World Cup. We have to see how he develops, how his rehab will develop."
Varane, who has suffered several long-term injury absences during his career, adds to France coach Didier Deschamps' headaches ahead of his naming his squad for the finals in Qatar on November 9.
N'Golo Kante, Chelsea's defensive midfielder who was a key part of France's success four years ago, will definitely miss the tournament with a hamstring injury.
Paul Pogba is a doubt as he is still recovering from knee surgery and AC Milan goalkeeper Mike Maignan, the backup to first choice Hugo Lloris, could be ruled out with a calf injury.
France's first World Cup group game is against Australia on November 22 before they face Denmark on November 26 and then Tunisia four days later.
Ten Hag said that Cristiano Ronaldo would be in the squad for Thursday's match -- a game his side need to win to stand any chance of topping their group.
That would allow them to avoid a third place side from the Champions League in February's play-off round.
Ronaldo returned to first-team training with Manchester United for the first time on Tuesday since his refusal to come on as a substitute against Tottenham last week.
The Portuguese was left out of United's squad for Saturday's 1-1 draw at Chelsea and did individual training with fitness coaches on Friday.
"It's not difficult (Ronaldo situation). We said everything, answered all the questions. He was out for one game and now back in," said Ten Hag.
"We have an important game tomorrow, we want to top the group."