The Sweden striker, who joined Milan at the end of the transfer window, scored both goals in his side’s 2-0 victory at the San Siro.
But afterwards he became embroiled in a heated discussion with the former Milan manager on the Mediaset Premium TV show.
Ibrahimovic, who formerly played for city rivals Internazionale, took exception when Sacchi joked that he would not have scored his first goal if he did not have such big feet.
"Sacchi needs to learn how to shut up," Ibrahimovic fumed. "He seems jealous because he talks too much.
"He needs to talk less about me on TV and in the newspapers. If he wants something he can come and see me about it. If you don't like the way I play, don't come and watch me.
"He also said things about me when I was at Barcelona."
Sacchi, who was a guest on the show, attempted to defend himself, insisting he had the right to "express my opinion in a polite manner".
Ibrahimovic continued his rant and Sacchi, 64, concluded by saying: "Learn some manners, son."