The 31-year-old batsman, who missed a four-day warm-up match in East London after suffering the injury during a nets session, will be replaced by Imran Farhat.
"The team management has told the national selectors that MRI scans have confirmed that Taufiq will require another three to four weeks to make a complete recovery. So he is returning home," a PCB spokesman said.
"In his place the selectors have picked Imran Farhat to reach South Africa before the first test."
Taufeeq has played 43 tests and scored 2943 runs at an average of 38.72.
His replacement in the tour match, Nasir Jamshed, is now in line to make his test debut after notching up two half centuries in East London.
The three-test series begins in Johannesburg on Friday.