Ajax were trailing 3-0 in the second half when the game was initially suspended in the 56th minute before being abandoned. The remaining minutes will now be played behind closed doors.
Ajax voiced disagreement with the KNVB's decision, citing scheduling concerns, and adding they were considering taking legal steps.
"The competition and Dutch Cup program is being adjusted for four clubs by the KNVB to play the remainder of a suspended match," the club said in a statement.
"Not only the clubs but also the supporters suffer the consequences of this."
The KNVB defended their decision in their own statement.
"The basic principle is that the competition must be as fair as possible and that a match should therefore preferably be decided on the field. The match must then be resumed as quickly as possible."
The Eredivisie match between Ajax and FC Volendam, initially scheduled for Wednesday, will be postponed to a later date.
Ajax, who have had a poor start to the season with just one win, sit 14th in the 18-team league. They finished third last season and failed to qualify for the Champions League for the first time in 13 seasons.