Television replays showed Bowyer, who is 34 on Monday, appearing to stamp on the knee of Gunners defender Bacary Sagna as he lay on the ground. In a separate incident Bowyer was shown to apparently catch Sagna down the back of his Achilles near the touchline.
Referee Peter Walton took no action at the time and Bowyer was eventually substituted by Birmingham manager Alex McLeish.
The FA will now contact Walton to find out whether or not he saw the incidents involving Bowyer during Arsenal's 3-0 win.
If Walton confirms he did not see what occurred, then the FA have the power to pursue the matter and to decide whether or not to charge Bowyer with violent conduct. If a charge was made and subsequently proved, then the former Newcastle and West Ham player could face a three-match ban.
Arsenal manager Arsene Wenger preferred not to highlight Bowyer's actions after the game. He said: "I do not want to talk too much about that because I haven't seen any replays. During the game, it was very difficult the challenge on Fabregas (by Roger Johnson) and Sagna (by Bowyer). I will watch that again and give you my opinion later."
McLeish said that he "did not see it" when asked about Bowyer's alleged stamp in his post-match press conference.