In a video circulating on social media, the midfielder could be seen lashing out at what appeared to be a Twente supporter in front of the Ajax team bus before an official intervened.
The Dutch international later apologised for the incident.
"Steven Berghuis on Monday agreed to a settlement proposal from the professional football prosecutor of three matches' exclusion, one of which was conditional," the KNVB said.
"He will miss the first three league matches of the 2023-24 season as a result. That includes the overflowing registration of his fifth yellow card..."
Berghuis joined Ajax from Feyenoord at the start of the 2021-22 season in a move that caused controversy in the Netherlands due to the intense rivalry between the clubs.
He was named Ajax's player of the season in a disappointing campaign in which they finished third in the Eredivisie, outside the two Champions League qualification spots for the first time since 2009.
