While it is a relatively short trip - England leave at the end of February, play three ODIs and return to the UK on March 10 - the decision to allow Bayliss to miss it provides a rare opportunity for a block of time to spend with his family in Australia.
England's limited-overs tour of India finishes on February 1 after three ODIs and three T20Is.
The decision is no surprise. With England's schedule increasingly resembling the never ending tour, the ECB is keen to avoid players or coaches suffering from burnout.
Farbrace has stood in as England's interim head coach previously. After Peter Moores was sacked in May 2015, Farbrace took charge for the Test and ODI series against New Zealand in which the side's limited-overs resurgence started.
Farbrace has been rested from the Test section of the Bangladesh tour. Ottis Gibson, the bowling coach, has stood in as Bayliss' assistant, while Worcestershire's director of cricket, Steve Rhodes, has joined the management team for a couple of weeks.
England face the longest home season in their history in 2017. It starts on May 5 with two ODIs against Ireland, encompasses the Champions Trophy in June, Test and limited-overs series against South Africa and West Indies and ends with a day-night game at the Ageas Bowl on September 29. They depart for a long Ashes tour shortly afterwards.