The 39-year-old striker was sent off on the hour mark with Milan 2-0 up.
Ibrahimovic saw red after he traded words with the match official.
Milan coach Stefano Pioli told Sky Sport Italia: “Zlatan told me that he argued with the referee and it lasted some time.
“He assured me that he did not disrespect him and above all he did not offend.”
Despite protesting his innocence, the Swede will miss Milan’s next game and be forced to pay the fine.
The club went on to win the game 3-1, but still trail rivals and league leaders Inter Milan by eight points.
Zlatan currently earns around £5.94million per season – or £114,000 per week.