Maxwell, who was replaced by top-order batsman D'Arcy Short, was only recalled to the Australian team earlier this month after taking a break last October to deal with mental health issues.
He will have surgery on Thursday and be out of action for between six and eight weeks, Cricket Australia said in a statement on Wednesday.
"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," national selector Trevor Hohns said.
"Unfortunately, the pain he has experienced in the elbow in the latter stages of the (Big Bash) increased over the weekend and he will have surgery immediately to rectify the situation."
Maxwell said he was disappointed to withdraw from the squad but having surgery was the right decision.
"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," he said.
Australia start the tour of South Africa on Feb. 21 with the first Twenty20 in Johannesburg before the one-day series starts in Paarl on Feb. 29 and concludes with further matches in Bloemfontein and Potchefstroom in early March.