Soon after City won 1-0 at Leeds last month, Farke made a beeline for the referee after the final whistle and was quickly shown a red card, with assistant manager Edmund Riemer suggesting what the German said was "too aggressive".
"It was alleged that the manager entered the field of play at full time to confront the match official/s, contrary to Law 12 of the Laws of the Game," the FA said in a statement.
"Daniel Farke subsequently admitted the charge against him and accepted the standard one-match suspension and 8,000 pounds fine."
Leeds are 15th in the league standings and next host Norwich City - a team Farke previously managed - in the fifth round of the FA Cup on Sunday.