Monkhorst joined the Hawks' ranks in 2010, while Otten, a former Adelaide Crow, arrived at Waverley in 2020 after the conclusion of his playing career, with both mainly focused on the development of the club's ruck department throughout their time at the club.
Hawthorn football boss Rob McCartney praised both Monkhorst and Otten in a club statement and wished them well for their future ventures.
"'Monky' has been a tremendous character to have around the club over his 13 years at Hawthorn. He has an outstanding ability to help build a strong culture whilst also strongly educating the players he works with," McCartney said.
"Andy has been with us for three years now and he has proven to be a valued contributor in our coaching ranks as well.
"We wish both Monky and Andy all the best in their future endeavours and thank them for their service to the club."
The Hawks did not announce who will fill the vacancies left by the departures of Monkhorst and Otten.