The world body did not say that the armbands breached its ban on wearing political symbols but the case is another step on the road to sanctions against the two countries.
"We can confirm that disciplinary proceedings have been opened on this matter," a FIFA spokesperson told AFP when asked about action planned after the November 11 match at Wembley.
FIFA said it would not comment further on the case "nor speculate on any outcome".
The players on both squads as well as England's interim manager Gareth Southgate wore the black armbands bearing the poppies at the Wembley game which England won 3-0.
November 11, Armistice Day, is the traditional day in Britain to pay tribute to all of the country's war dead.
Northern Ireland and Wales had also wanted to wear the poppy tributes but after consulting with FIFA wore just the black armbands with no poppies.
FIFA rules ban "political, religious or personal slogans, statements or images" on player kits.
Sanctions could go as far as having points deducted in their World Cup qualifying group but a fine is considered more likely.
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