Brown was found guilty of breaching three rules following a disciplinary tribunal at Hampden.
The SFA panel found him guilty of not acting in the best interests of football by making "insulting" comments about Rab Douglas in accusing the former Dens Park goalkeeper of "telling lies" over his acrimonious exit from the club.
The former Rangers player was also found guilty of a similar charge and of making "offensive comments suggesting the use of violence" over an extensive interview about the Ibrox club last month.
Brown spoke out after former chief executive Charles Green - following his ill-fated appointment as a consultant to Rangers - repeated his claim that last season's Light Blues team was the worst ever and that manager Ally McCoist faced a problem if he did not win a major cup competition this season.
Rangers were knocked out of the Scottish League Cup by Forfar on the day the interview appeared.
The following week, Brown gave an interview which appeared in several newspapers in which he said: "Green's comments were a disgrace. If my own directors had said that about me, I would have taken every one of them by the throat."
Brown's three-match ban is suspended until the end of this season.