The explanation was deemed necessary by the midfielder after footage of him appearing to spit at Ballack when the Germany captain was playing for Bayern Munich against Arsenal in 2005 was available on YouTube.
An FA spokesman said the governing body had written to Hull asking the Premier League club to officially give its version of events after Brown alleged Fabregas spat at Horton in the tunnel at the Emirates Stadium after the match.
Arsenal won 2-1 with a hotly disputed goal by William Gallas that Brown thought was clearly offside.
"Once they have given us their account of events we will decide what action to take," the FA spokesman added.
He also said the fact the referee did not mention the incident in his match report did not mean Fabregas, if he did spit, would escape punishment on a technicality.
"There is no obligation on the referee to be in the tunnel for 15 minutes or half-an-hour after the game," he said.
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Regarding the footage showing Fabregas appearing to spit at Ballack, the Arsenal player told The Sun: "I have seen this video on the internet many times before and I remember the incident clearly.
"It was four years ago and I leant over Michael Ballack who was playing for Bayern at the time and I shouted at him because I felt like I did not make a bad tackle and I felt that contact was minimal.
"I did not spit at him. It happens during matches that sometimes you have heated exchanges with your opponents. I am not proud of it but I was 17. The referee saw it and gave me a yellow card."
He then added: "The simple fact is I did not spit at the assistant manager of Hull City.
"I absolutely and categorically deny that I spat at anyone and cannot understand why Hull are making these allegations about me.
"I have never spat at anyone in my life. It is a disgusting habit. Why would I do something like that after a match I was not even playing in.
"I was on the pitch at the end of the game celebrating with my team mates but I promise I did not do anything wrong. I have nothing to hide and nothing to be ashamed of."
Brown, asked by reporters on Wednesday what the specific complaint was, replied:
"One, being on the pitch after the game. Two, dressed in the way he was dressed. Three, the pictures in the national papers verify the aggression he was showing towards players and staff after the game.
"I could go on but I am not one for crying over spilt milk. Whichever way you want to look at it, he addressed that spitting incident at my assistant manager who has managed probably 1,200 games in his career. Disgraceful act."
Fabregas has not played for Arsenal since damaging a medi
