Johnson is due to return for the upcoming World Twenty20 but, after spearheading Australia's Test series wins over England and South Africa over the past three months, is set to be given time off.
Johnson took a remarkable 63 wickets in eight Tests over the winter and was crowned Australia's player of the year in January.
The left-armer will fly back to Australia before the first match of the Twenty20 series against the Proteas, which begins in Port Elizabeth on Sunday.
"Mitch has had a very long summer and we think he will benefit from returning home for a few days of rest with his family where he can freshen up," coach Darren Lehmann said.
"He will link back up with the squad in Bangladesh ahead the ICC World Twenty20."
All-rounder Moises Henriques will stay on in South Africa as a replacement for Johnson.
The three-match series is Australia's final warm-up for the World Twenty20, which begins on March 16.
- Sports & Recreation