The incident occurred in the 61st minute of Republic of Ireland's 1-0 victory in Cardiff but referee Damir Skomina did not see it.
A FIFA spokesperson confirmed they are currently collating evidence to see whether Brady should be charged.
If the governing body decide to charge Brady, he could miss at least the first leg of their World Cup play-off next month.
The Burnley midfielder only just returned from a one-match suspension for Ireland's must-win match in Cardiff, where James McClean's second half strike secured second place in Group D, ahead of their opponents on the night, Wales.
Speaking on 'Sky Sports' after the qualifier, former Wales forward Craig Bellamy said there was "no chance" Brady deserved to be suspended.
Martin O'Neill will definitely be without David Meyler for the first leg of their play-off, which is due to take place between November 9 and 11, after the Hull City midfielder picked up a booking in injury time for a challenge on goalkeeper Wayne Hennessey. It was his second yellow card of the World Cup qualifiers, meaning he will now serve a one-match suspension.
The draw for the World Cup play-offs takes place on October 17.