Balotelli - a former Inter player - was targeted for abuse during a 1-1 draw, and Serie A officials met on Tuesday to decide on a punishment.
The Italy striker has also been fined - £8,600 - for a gesture towards Inter supporters at the final whistle, while Milan must hand over the same amount after their fans displayed "insulting banners".
Inter's latest penalty comes just weeks after fans sang derogatory songs about the striker during a game against Chievo, costing their club £13,000.
President Massimo Moratti apologised and called for the chants to stop in the aftermath of that incident, but some supporters failed to heed his warning.
Racism has increasingly been in the spotlight in Italy in recent months, and Milan's Kevin-Prince Boateng walked off the pitch in response to taunts during a January friendly against Pro Patria.