Both countries chose to defy FIFA by wearing poppies in Friday's Group F match to commemorate the armistice that ended World War One.
"We can confirm disciplinary proceedings have been opened on this matter," a spokesperson for soccer's governing body said on Thursday.
"Please understand we cannot comment further at this stage nor speculate on any outcome or provide an estimated timeline."
FIFA rules forbid players from wearing anything that can be perceived as a political statement.
(Reporting by Toby Davis; Editing by Tony Jimenez)
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