Fans of both teams displayed a poppy mosaic ahead of their respective fixtures against Serbia and Azerbaijan over remembrance weekend, during which black armbands were worn.
England and Scotland both wore the symbol on armbands, vowing to accept any sanction, and are already confirmed to be under investigation.
International Football Association Board (IFAB) rules state that players must not wear "political, religious or personal slogans, statements or images".
A FIFA spokesman said: "The Disciplinary Committee decided to open proceedings against the Irish Football Association and the Football Association of Wales in relation to several incidents involving the display of signs reported after the matches Northern Ireland-Azerbaijan and Wales-Serbia respectively."
The IFA has vowed to "robustly defend" the charges levelled against it, while the FAW is yet to comment.