Australian Montemurro, who left Melbourne City to join Arsenal in 2017, guided the north London outfit to their first WSL title in seven years in 2019, as well as reaching four cup finals and a Champions League quarterfinal.
Arsenal said Montemurro has decided to take a professional break to "recharge and dedicate more time to spending with his family."
"This has been the hardest professional decision of my life, as I absolutely love this job and this club, the club I have supported all my life." Montemurro told the club's website.
"I'm hugely grateful to the club for their unrelenting support during my time here and in understanding and respecting my decision.
"My focus now is helping the team to complete the season strongly and finishing as high as possible in the WSL, leaving the club in good shape for the future."
Arsenal sit fourth in the WSL table, three points adrift of third-placed Manchester United, who occupy the final Champions League qualification spot.