The decision was taken after a 1-1 draw with lowly Volendam left Ajax fifth in the Dutch top-flight and seven points adrift of leaders Feyenoord.
“This is a painful decision, but it’s necessary,” said Ajax chief executive Edwin van der Sar.
“Regardless of the good start to the season, we lost a lot of unnecessary points. The football itself was precarious too.”
Ajax’s last win was a 3-1 victory against Rangers in the Champions League on 1 November but they failed to reach the last 16 of the competition and have dropped down into the Europa League.
They followed that game with one loss and six successive draws in the Eredivisie, ending with the most-recent result against third-from-bottom Volendam.
Ajax sold winger Antony and defender Lisandro Martinez last summer, while striker Sebastien Haller, midfielder Ryan Gravenberch, left-back Nicolas Tagliafico and defender Daley Blind also left the club under Schreuder’s tenure.
“We gave Alfred our time and trust to change the way things were going. It became clear to us that he could not change the tide,” added Van der Sar.
“Regardless of the many transfers that took place, we consider the squad fit for a championship. We lost a lot of points over the last few weeks and sadly saw a lack of progression.”