The pair were called to a Scottish Football Association disciplinary hearing at Hampden after being sent to the stands in the latter stages of their team's Scottish Premiership meeting last month
McInnes pushed Brown after the Hearts coach entered the opposition technical area while celebrating his team's late winner.
Brown, who signed a short-term contract with Hearts on Wednesday after working for free for several months, then remonstrated with Aberdeen counterpart Tony Docherty before going down the tunnel.
The 62-year-old admitted ''misconduct at a match by leaving the technical area in the absence of special circumstances and by adopting an aggressive attitude to a member of the opposing team staff''.
McInnes admitted a charge of ''misconduct at a match by adopting an aggressive attitude to a member of the opposing team staff''.