The board said no replacement will be brought in for Rabada as there is an extended squad in place in the Bio-Secure Environment (BSE), but George Linde has been retained from the Test team as an extra spin-bowling option for the series.
South Africa will be led by captain Quinton de Kock as they come off a 2-0 home series win over Sri Lanka that concluded on Tuesday.
South Africa won their T20 series against world champions West Indies and Ireland, and will once again be captained by Temba Bavuma in both formats.
South Africa spinners Tabraiz Shamsi and George Linde stifled West Indies' chase as the visitors claimed a 16-run victory in the second Twenty20 international on Sunday to level the five-match series at 1-1.
South Africa have recalled top-order batsmen Faf du Plessis and Rassie van der Dussen for their three-match One-Day International tour of India later this month, while left-arm spinner George Linde is named in the squad for the first time. The squad will be captained by Quinton de Kock and play the first ODI in Dharamsala in March 12.
Meanwhile, South Africa have included uncapped off-spinner Prenelan Subrayen and seamer Lizaad Williams in their squad for the two-Test series in the West Indies that starts on June 10.
In pursuit of a 234-run target, India were cruising nicely at 155 for 3 in the second innings when bad light forced an early stumps.
Seamer Mark Adair (3-39) was the pick of the home bowlers with his changes of pace, while off-spinner Simi Singh (2-19) again impressed with his accuracy and variations.
South Africa have named three front-line spinners in their squad for the Twenty20 World Cup in the United Arab Emirates and Oman but left out opening batsman Janneman Malan.
He joins injured fast bowler Kagiso Rabada on the sidelines.
Fast bowler Duanne Olivier has been recalled for South Africa's home Test series against India, a reward for excellent domestic form from a player who shot to prominence four years ago before taking up a Kolpak contract.
The loss of Bavuma will further weaken their top six, especially as the experienced Reeza Hendricks has withdrawn from the squad after the birth of his first child, while the in-form Rassie van der Dussen is doubtful for the first match of the series, at least, with a grade one left quadriceps strain.
Aiden Markram struck a brisk half-century as the hosts levelled the four-game Twenty20 International series against Pakistan
Captain Kieron Pollard impressed with bat and ball as West Indies defeated South Africa by 21 runs to level the five-match Twenty20 series at 2-2 on Thursday.
Rohit scored 212 and Ajinkya Rahane contributed 115 as India declared their first innings at 497 for 9. South Africa are 9 for 2 at close of play.
Hanuma Vihari got some runs coming as India A scored 198 for 5 at stumps against South Africa A on the second day of the second unofficial Test, in Bloemfontein, on Wednesday. Vihari was batting on 45 at close of play, having found the fence six times while facing 146 balls.
Young Ishan Kishan blasted a blistering 24-ball 55 as India 'A' beat South Africa 'A' by two wickets in the rain-hit second unofficial ODI to take a 2-0 lead in the five-match series.
Maharaj sustained an injury to his right shoulder while fielding on Day 2 of the second match
Local hero Sanju Samson struck a blistering 48-ball 91 as India A romped to a 36-run victory over South Africa A in the fifth and final unofficial ODI, helping the hosts claim the series 4-1, in Thiruvananthapuram, on Friday.
Saha was hurt in the 27th over, while keeping to off-spinner Ravichandran Ashwin.
Pakistan set South Africa a daunting target of 370 to win the second and final Test in Rawalpindi
Jonny Bairstow bludgeoned a brilliant unbeaten 86 from 48 balls as the tourists chased down 180 to beat South Africa by five wickets
A complete list of players, who failed to attract any bid in the IPL 2021
At stumps, Pakistan's score read 145/3 with Fawad and Babar unbeaten on 42 and 77 runs respectively. For South Africa, Keshav Maharaj picked two, Anrich Nortje took one while Kagiso Rabada went wicketless.
Pakistan had been reduced to 76 for five in their second innings as South Africa's spinners made inroads through the top order having been bowled out for 201 in another shambolic display with the bat.
Becomes only the 3rd Indian batsman to be in the top-10 in all formats of the game; Rahane at career-best fifth
Led by Quinton de Kock, South Africa's 44 cricketers, who are part of a men's high performance squad, have returned to training amid the COVID-19 pandemic after getting approval from the country's sports ministry. South Africa has reported more than 1,38,000 COVID-19 cases with over 2,400 deaths.
Himachal Pradesh Cricket Association (HPCA) general manager Col HS Manhas said all precautions are being taken by the medical teams amid the coronavirus scare.
With 762 points, Kohli is behind England's David Malan
For South Africa, Rassie van der Dussen has advanced three slots to the sixth position, just one shy of his career-best, after scores of 34 not out and 52.
Dawid Malan returned to his home town on Sunday to steer England to a four-wicket win over South Africa in their second Twenty20 international in Paarl as they clinched the three-match series.
Rajneesh Gupta has all the numbers about how each player from the Indian and South Africa teams fared in T20 Internationals.
South Africa captain Faf du Plessis walked for the toss along with Temba Bavuma as the proxy captain, who was given the responsibility of calling the toss.
Replying to India's 497-9 declared, South Africa were all out for 162
South Africa will have to produce an exceptional batting performance to get back into the contest when skipper Faf du Plessis and Zubayr Hamza return to the crease in Ranchi on Monday.
The unbeaten Mumbai duo added 185 runs for the fourth wicket to rescue the hosts who looked in dire straits at 39 for three in the morning session after opting to bat in Ranchi.
India's formidably consistent match-winners have a date with history in the New Year when they take on an out-of-sorts South Africa in the second Test in Johannesburg from Monday in pursuit of a coveted first-ever series win in the Rainbow Nation.
Dube smashed an unbeaten 45 off 28 balls while Pandey plundered 81 off 59 balls as India A overcame a poor start to win the rain affected match rather comfortably in the end. Chasing 208 in 30 overs, India A reached the target in 27.5 overs.
India have a real shot at winning their first ever away series against South Africa,
Virat Kohli's talismanic presence will be the shot in the arm that India would need in their bid to win the historic first-ever away Test series against South Africa.
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