The Swindon Town director of football blasted the official during the half-time interval of his side's 1-0 loss to League One relegation rivals Bury at Gigg Lane in February.
Brown awarded the hosts a penalty late in the first period after Raphael Branco was penalised for pulling an opponent's shirt in the box.
Sherwood was furious with the decision and launched into a foul-mouthed rant, according to The FA's written reasons for his suspension.
Referee Mark Brown's report
Submitted to the FA Regulatory Commission
"After the half time whistle, and as I was walking down the tunnel Tim Sherwood of Swindon Town approached me and said 'You're the only f***** in the ground that's f****** seen it you f****** mug'. He then started pointing aggressively in my face.
"I told him to calm down and stop pointing at me or he would be sitting in the stands for the second half. He then continued 'I wasn't even in the dugout you f****** mug and you would be doing me a favour'.
"I told him I wanted to speak to him at my dressing room but he ignored me and walked off towards the Swindon changing room. I followed him and stood outside and told the coaching staff I wanted Mr Sherwood to come outside as I needed to speak to him.
"After approx 45 seconds Mr Sherwood walked out and walked past me and I informed him 'that he would be reported for his comments towards me'.
"His reply was 'f*** off you mug'. I then entered my dressing room area and informed the stewards of my decision and that if Mr Sherwood tries to come down into the technical area he should not be allowed."
Sherwood admitted the charge and agreed to a paper hearing, and the former Tottenham manager was fined £2000 and warned as to his future behaviour.