Former captain Dravid sustained a fractured jaw after scoring a century in the second test against Bangladesh in Dhaka while Yuvraj suffered a wrist injury during India's 2-0 rout of Bangladesh.
Both have been ruled out of the highly-anticipated two-test series between the top two teams in the official test rankings.
The second test will be played in Kolkata from Feb 14-18.
"Rahul Dravid... has been advised rest for three weeks," an Indian cricket board statement said on Thursday.
"Yuvraj Singh has also been ruled out of the test series due to an injury to his left wrist," the statement added.
Dravid was hit on the face by a bouncer from paceman Shahadat Hossain, forcing the batsman to retire hurt on 111.
Uncapped Subramaniam Badrinath has been drafted to bolster the batting in the absence of Dravid along with two other new faces in fast bowler Abhimanyu Mithun and wicketkeeper-batsman Wriddhiman Saha.
Karnataka bowler Mithun takes the place of Shanthakumaran Sreesanth who suffered a hamstring injury. Saha has been included as second wicketkeeper.
India drew a three-test series 1-1 by winning the final test during South Africa's previous tour two years ago.
South Africa also play three one-day internationals on their month-long tour.
Squad: Virender Sehwag, Gautam Gambhir, Murali Vijay, Sachin Tendulkar, Vangipurappu Laxman, Subramaniam Badrinath, Mahendra Singh Dhoni (captain), Harbhajan Singh, Zaheer Khan, Ishant Sharma, Amit Mishra, Sudeep Tyagi, Pragyan Ojha, Abhimanyu Mithun, Wriddhiman Saha.