Monash IVF CEO Michael Knapp made the decision to step down in a move supported by the board, the company said on Thursday.
Mr Knaap, who was also a director, was appointed CEO in 2019 and led the company through a period of "significant growth and transformation".
The company's chief financial officer, Malik Jainudeen, will step up as acting CEO in the short term.
Monash IVF earlier this week revealed that staff at its Melbourne clinic had recently transferred the wrong embryo to a woman, giving her one of her own rather than one from her partner, as they had requested.
The pair is believed to be in a same-sex relationship.
The company, which is based in Melbourne but has clinics around Australia, apologised to the couple and launched an internal investigation.
The Victorian Health Regulator is also conducting its own probe into how the error occurred at the clinic in the suburb of Clayton.
In April, Monash IVF revealed a woman at its Brisbane facility had another patient's embryo transferred to her, which it blamed on "human error".
The mistake was picked up in February after the birth parents asked for their remaining embryos to be transferred elsewhere and an extra embryo was found in storage.
Monash IVF apologised, expressed confidence that it was an isolated incident and hired leading barrister Fiona McLeod to lead an independent review, which has now been expanded.
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