The Brazilian player was sent off towards the end of the match after he spat at Sassuolo midfielder Federico Di Francesco.
The Italian soccer federation announced Costa’s punishment on Tuesday, following a review of the referee’s match report and video evidence.
He was charged with violent conduct and will miss out on matches against Frosinone, Bologna, Napoli and Udinese.
Juventus manager Massimiliano Allegri agreed that Costa’s behaviour was unacceptable.
“It is only right that he is fined and he certainly will be,” Allegri said after the match.
“I was surprised by his reaction. We have suffered a goal, a red card and a suspension, which will be long.”
While Costa has apologised for the incident on social media, he has also defended his actions by claiming that Di Francesco directed a racial slur towards him.
Di Francesco has strongly refuted his opponent’s allegation.
“I won’t allow racist behaviour and/or phrases to be attributed to me, which do not belong to my ethical values and are the fruit of other people’s imagination,” the 24-year-old said.
“I am deeply disturbed by the innuendo and inventions that have appeared in some national media.
“All this is offensive and derogatory.”
