The France striker, who has struggled for fitness all season, missed his side's 3-0 home league win over rivals Tottenham Hotspur on Saturday because of a neck injury.
"As you know he keeps picking up niggling injuries which are down to fatigue," Wenger was quoted as saying on the club's Web site www.arsenal.com.
"The medical team has now assessed the situation and although it's difficult to predict exactly, Thierry will be out for at least a few weeks, as we need to give him time to fully recover."
Henry, 29, told Monday's issue of French sports daily L'Equipe that a demanding schedule of matches this year had taken its toll.
"After 60 matches in 2006, comes a time when your body tells you to stop and you have to listen," Henry, who said he was suffering from a sore left thigh muscle, told the newspaper.
"I have to say stop for a month, maybe a month and a half, the time for the pain to disappear."
Arsenal face Porto in the Champions League on Wednesday, a match that Henry was due to miss anyway because of suspension.
Their next Premier League game is against champions Chelsea at Stamford Bridge on Sunday. Arsenal are third in the standings, 16 points behind leaders Manchester United with a game in hand.
(Additional reporting by Patrick Vignal in Paris)
