The Daily Mail reported that "the FA have a dossier of evidence regarding supposed corruption, including alleged phone messages before kick off at the Kassam Stadium which claim that Brown would be booked in a betting scam that allegedly cost one bookmaker more than £1,600."
The Northern Ireland defender received a yellow card in the 59th minute of the match after fouling Bukayo Saka (21) with the score 0-0 at the time.
An FA official told Reuters that the governing body was aware of the matter and would investigate.
In a statement on Wednesday, Brown's club said: "Oxford United can confirm that they have been made aware of a specific allegation of irregular betting around our Emirates FA Cup game against Arsenal on Monday evening.
"The club will co-operate fully with any investigation and while this is ongoing, we are unable to make any further comment."
