Steijn, who took over from Johnny Heitinga this summer, has won just two of his 11 matches across all competitions this season.
A 4-3 defeat at Utrecht on Sunday, left Ajax second bottom on the Eredivisie table.
It was their fourth loss in seven top flight matches this season.
Ajax have won none of their last eight matches across all competitions.
On the club's official website, managing director Jan van Halst said: "We have worked intensely and professionally together over the last few months. But the sportive successes and the development of the team were lacking.
"That is why we decided to sit down together again today. This time, Maurice also expressed his concerns on whether he was the right man in the right place. Together, we decided that it would be best to part ways. Hedwiges Maduro will do the honours for the coming period."
Steijn added: "This morning, I sat down with the board, and we continued our talks later this afternoon. We came to the conclusion that this is what is best for Ajax, although I regret that.
"Everyone who knows me knows I have done everything to take Ajax back to the place where this club belongs. But I failed to do so. I want to thank the supporters and the people I have worked with here, and I hope Ajax will find its way up again soon."
Ajax will travel to Brighton in the Europa League on Thursday.
