Koulibaly was subjected to monkey noises from the crowd several times during Inter's 1-0 win at the San Siro on Wednesday, leading Napoli to ask for the match to be halted, without success.
Inter will also have to play another game with their North Stand closed.
In its statement, the league's disciplinary body mentioned "offensive songs of a racist nature towards Kalidou Koulibaly", but also "insulting songs of a territorial nature" towards Napoli fans.
Senegalese centre-back Koulibaly will have to serve a two-match ban for his sending off, after seeing a second yellow card for sarcastically applauding the referee.
Koulibaly apologised on Twitter for the defeat and being sent off but said: "I am proud of the colour of my skin. (Proud) to be French, Senegalese, Neapolitan: a man."
Napoli coach Carlo Ancelotti revealed that the club's staff had asked the referee three times to suspend the match because of the chants.
"The solution exists," Ancelotti told Sky. "You have to stop the match. You just have to know when, after how many announcements. And if we don't know, then next time we may have to stop play ourselves."
Milan mayor Guiseppe Sala apologised to Koulibaly for the abuse, asking the 27-year-old for forgiveness.
"The boos aimed at Koulibaly were shameful," said Sala on Facebook.
"A shameful act towards a true athlete who wears the colour of his skin with pride.
"I apologise to Kalidou Koulibaly on my own behalf and on behalf of the people of Milan who testify to the feeling that we are brothers even in these difficult times."
It was a match that was also marred by pre-match violence which saw an Inter fan die after being struck by a vehicle.
Milan police chief Marcello Cadorna told journalists that the incident happened after around 100 Inter fans attacked Napoli supporters' minibuses with chains and hammers.