The chants occurred during the Nerazzurri's clash against Chievo at San Siro on Saturday that ended in a 3-1 victory for the home side.
Balotelli, who joined AC Milan from Manchester City last month, was on Inter's books between 2006 and 2010.
"A fine of €15,000 has been issued to Inter Milan for having supporters who, in the 41st minute of the first half and the 42nd minute of the second half, directed expressions of racial discrimination to the player of another club," reads a statement on Lega Serie A's official website.
Inter president Massimo Moratti was quick to condemn his club's supporters' behaviour.
"I was told about it because I couldn't make out clearly what they were saying," he said. "I'm very sorry about that.
"I'm very sorry and I really hope it doesn't happen during the derby [on February 24]."