Gennaro Gattuso's side battled to a 1-0 win over Lazio on Saturday, with Kessie's penalty enough to secure the full three points for the hosts in the battle for top four.
Before the match, Bakayoko and Acerbi engaged in a media back-and-forth which added some extra spice heading into the match.
The Lazio defender stated prior to kick off: "We are inconsistent, but we go to San Siro to win. We are stronger, there is no comparison to individuals."
This led to Bakayoko disagreeing and responding on social media, with the Chelsea loanee telling Acerbi: "See you Saturday."
Ok ACERBI see you Saturday ☺️— T.Bakayoko14 (@TimoeB08) April 9, 2019
Following full-time at the San Siro, Kessie and Bakatoko celebrated their hard-fought victory by raising Acerbi's exchanged shirt in front of their home supporters.
This, unsurprisingly, angered Acerbi after the match with the 31-year-old making his opinion known to the public.
"I'm sorry because I exchanged the shirt to put an end to the [social media] matter," he said. "Fomenting hatred is not sport but a sign of weakness."
The AC Milan duo then responded to Acerbi's grievance, with both apologising to the Lazio star on social media in the aftermath of the incident.
"Mine was a playful gesture I didn't want to disrespect anyone," Bakayoko said . "I beg your pardon if you felt offended."
And Kessie wrote : "My sincerest apologies to Acerbi, respect for all."
With the three points, AC Milan now hold fourth position in the Serie A table on 55 points while Lazio sit in eighth on a tally of 49.
AC Milan and Lazio are also set to meet again in the coming weeks with both set to face off in their Coppa Italia semi-final second-leg on April 24.
They battled to a 0-0 draw in their first meeting back on February 26, but Gattuso's men will be optimistic of another win following Saturday's result.