Wenger said he was hoping to know more from the results of a scan which Henry, the club's main goalscorer, was having on a groin injury on Friday.
Asked if the France forward would be fit to face United at the Millennium Stadium in Cardiff, Wenger told Sky Sports News: "I don't know yet. It's impossible to say today."
Speaking to reporters at Arsenal's training ground, Wenger said: "Thierry is definitely out for the next two games and how long he will be out for in total I do not know.
"He won't be out for three months, but it might be three or four weeks and the final is on May 21 which is not far away."
Henry missed Arsenal's 3-0 FA Cup semi-final victory over Blackburn Rovers last weekend, along with the 0-0 draw at Premier League leaders Chelsea on Wednesday.
They were rare absences for a player who has been the Premier League's top scorer in two of the last three seasons and has been pivotal to the champions' domestic success.
"This injury has come about because he has pushed his body too much, but it is always very difficult to give him a rest," Wenger said.
CAMPBELL AVAILABLE
The Arsenal manager said England defender Sol Campbell was fit to return from injury to face his old club Tottenham Hotspur in Monday's north London derby.
Campbell has not played for two months due to an ankle injury and Wenger has been taking his time before bringing him back. The 30-year-old was injured in October just a month after returning from a three-month layoff.
"I rushed Sol Campbell back before and it did not help him," Wenger said. "He is a massive player and it is always tempting to put him in there, but (Kolo) Toure and (Philippe) Senderos have done well and we will keep our defensive stability.
"For me Sol is still in the England team and the ideal historical pair have been him and Rio Ferdinand. John Terry (of Chelsea) has done well and is coming into his good years at 24 years old, but Sol has the experience."
Sweden midfielder Fredrik Ljungberg is out of the Spurs game, having missed training all week with a hip problem.
The match at Highbury could seal the league title for Chelsea if Arsenal fail to win and Jose Mourinho's men beat Fulham on Saturday.
