The 27-year-old had struggled with the injury throughout the tour and could bowl only three overs during practice on Tuesday.
When a fitness Test was abandoned on Wednesday because of poor weather, the management decided to send him home.
Nel will be replaced by Eastern Cape swing bowler Charl Langeveldt, who is on tour with the A team in Zimbabwe.
Langeveldt will travel via Johannesburg and Dubai before arriving on Saturday.
"Nel was supposed to complete a second fitness Test on Wednesday but it was glaringly obvious that he wasn't right," spokesmen Moabi Litheko said.
South Africa's lost the two-match Test series 1-0.
