Brown was shown a yellow card in the 59th minute of Monday’s third-round tie for a foul of Bukayo Saka with the score at 0-0.
The FA are said to have seen alleged phone messages before kick-off at the Kassam Stadium which claim that Brown would be booked as part of a betting scam.
One message is said to show a betting slip with about £200 staked on Brown being booked at odds of 8-1.
It is unclear how many bets were placed on the incident but one bookmaker is said to have paid out £1,600, and a spot-fixing investigation has been launched by the FA.
A report by the Daily Mail says the FA have a dossier of evidence regarding supposed corruption.
A statement from Oxford to Press Association read: "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."
Brown, a 24-year-old Northern Ireland international, was part of an Oxford side that frustrated Arsenal until just after the hour mark when the Premier League broke the deadlock through Mohamed Elneny.
Eddie Nketiah then struck twice in six minutes against the League One club, as Arsenal booked a fourth-round tie against Manchester City later this month.
Before then, Mikel Arteta’s side face Premier League games against Tottenham and Manchester United as they bid stay ahead of second-placed Manchester City in the title race.
On Sunday at Spurs, Arsenal will be seeking revenge for the 3-0 defeat they suffered against their north London rivals at the end of last season. Spurs went on to pip Arsenal to Champions League qualification.
Elneny said after Monday’s victory: “It was important for us to win because we have a derby in the next game, and we go there with the confidence to win away from home. We know it’s a special game for all of us in the derby, and we will go there full of confidence and we’ll go for three points.
“We knew it was going to be a tough game today because for [Oxford] it is one game of the season and it is something big for them. That’s why they gave everything in the game, and we had to manage this and come here to win to go through to the next round.”