With only two wins in their last 11 games, Leeds are close to the relegation zone and the pressure has been getting to Farke and his side in recent weeks.
The hard-fought 1-0 loss in the Premier League seemed to be breaking point for Farke as he was shown a red card by match official Peter Bankes after his actions which he defended at the time.
“I'm not light like a butterfly. I don't look unbelievably cute and sweet when I jog," he said. "I will never ever jog on the pitch again.
“There was not one bad word. I didn't abuse him at all. I didn't swear at him at all. As soon as I arrived, he had the red card in his hand.”
An FA statement said Farke admitted the misconduct charge and "accepted the standard one-match suspension and £8,000 fine".
This means Farke will not be on the touchline for Leeds FA Cup fifth-round tie against his former side Norwich City at Elland Road on Sunday as the side aim to book a place in the Quarter Final.
Leeds lost 1-0 to Sunderland at home Tuesday and is just three points above the relegation zone as they aim to rotate their side against Norwich who are 17th in the Championship.
He will return to the touchline for the Premier League encounter with Crystal Palace on March 15th as he aims to save his side from a relegation scrap.