The absence of the France striker, the English Premier League's top scorer with 25 goals, is a big blow to the champions for whom the game in Cardiff represents their last route to a trophy this season.
Arsenal will also be without England centre back Sol Campbell who has failed to recover from an ankle injury in time.
"Henry is out with a groin problem," Arsenal manager Arsene Wenger told reporters at Arsenal's training ground on Friday.
"It is an inflammation of his groin. We have to check that by scan today to find out how long he will be out.
"He could be out for a few weeks, he could be out for a few days. It could be quite serious.
"It is a big blow. We wanted Thierry with us but on the other hand we have to focus on the strengths we have and make sure we have enough to go through."
Campbell, Arsenal's defensive rock, has not played since February 1 due to an ankle injury. Wenger said: "Campbell practises and is close to full, full competitive fitness, but he is not involved."
Ivory Coast international Kolo Toure and Swiss Philippe Senderos are likely to play in central defence.
Wenger will be able to select Swedish midfielder Freddie Ljungberg, who has happy memories of Cardiff after scoring a spectacular goal in Arsenal's 2002 FA Cup final win over Chelsea. He has shaken off a hip problem.
Spanish striker Jose Antonio Reyes and Brazilian midfielder Edu have recovered from knocks although goalkeeper Manuel Almunia has a groin injury and full back Gael Clichy is out after foot surgery.
