Togo striker Emmanuel Adebayor scored in the first-half of his debut for the Gunners before Henry sealed the victory two minutes after the hour.
Birmingham striker Emile Heskey was sent off after 83 minutes for a second bookable offense.
The win put Arsenal in fifth place in the Premier League table with 40 points while struggling Birmingham were left in 18th place with just 20 points.
Adebayor broke the deadlock in the 21st minute when Vasiriki Diaby moved down the left flank and sent a shot that was cleared by Birmingham keeper Maik Taylor into the path of Adebayor who headed home easily.
In the 62nd minute, Francesc Fabregas released compatriot Henry who raced through on goal before firing a low shot past the hapless Taylor.
Elsewhere, Newcastle skipper and newly assigned assistant coach Alan Shearer reached a milestone.
Shearer scored a 64th minute goal in Newcastle's 2-0 over Portsmouth to overtake Jackie Milburn's record of 200 goals for the Magpies.
Charles N'Zogbia had opened the score in the 40th minute for the home side, who fired manager Graeme Souness in midweek.
This was the first win for Newcastle in seven league games.
In other matches, Bolton drew 1-1 with Wigan, Everton beat Manchester City 1-0, Aston Villa thrashed Middlesbrough 4-0, West Bromwich Albion defeated Blackburn 2-0 and West Ham cruised past Sunderland 2-0.