D'Arcy Short will replace Maxwell in both the T20I and ODI squads for the six-match South African campaign, reports cricket.com.au.
The 31-year-old will have surgery on the joint on Thursday in Melbourne. The Melbourne Stars captain had been carrying the injury for the back-end of the BBL season that his side finished as runners-up.
The operation and subsequent recovery is set to sideline Maxwell for six to eight weeks, but he is expected to be available the Indian Premier League (IPL) which starts March 29.
Maxwell said the decision to stand down from the Proteas tour was difficult but was worried he would not be at his best for international cricket.
"I was not confident that I could perform at international level with my elbow in its current state and have decided to undergo surgery straight away to fix the issue," the all-rounder said in a statement.
He further tweeted: "Shattered to be missing the South Africa tour. I wish all the lads the best of luck over there and I'll be watching from home."
"We are disappointed to lose Glenn this close to the tour as we were looking forward to welcoming him back to the national side in both the 20- and 50-over formats after his break during the summer," Australia's National Selector Trevor Hohns said.
"Unfortunately, the pain he has experienced in the elbow in the latter stages of the BBL increased over the weekend and he will have surgery immediately to rectify the situation.
Australia will take on the Proteas in a three-match T20I series and as many ODIs, starting February 21 in Johannesburg.