After opting against appointing long-term caretaker boss Johnny Heitinga on a permanent basis, the Ajax board brought in Steijn after he impressed during a one-year stint with Sparta Rotterdam.
However, in his first 11 matches in charge, Steijn was only able to deliver two victories, one of which came in the Europa League qualifying rounds.
The Dutch giants are currently on a run of eight matches without success in all competitions, with five defeats being posted during that period.
FC Utrecht inflicted Ajax's most recent loss on Sunday, withstanding a second-half fightback from their struggling opponents before prevailing 4-3 in a game that saw delays during the closing stages due to missiles being thrown onto the pitch.
With just five points from seven matches in this season's Eredivisie, Ajax sit second-bottom in the standings, an astonishing 22 points behind leaders PSV Eindhoven albeit with two matches in hand.
Although Ajax are currently preparing for an important week of action with fixtures against Brighton & Hove Albion and PSV Eindhoven respectively, Steijn has been removed from his position in the dugout.
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."
While Steijn has been judged on his results during his time in Amsterdam, the 49-year-old watched Ajax sell a number of the club's star men during the summer transfer window.
Jurrien Timber, Calvin Bassey, Edson Alvarez, Davy Klaassen, Dusan Tadic and Mohammed Kudus all left for pastures new, with their respective replacements yet to collectively make a positive impression.