Rabada, 22, pleaded guilty to using "inappropriate language" after dismissing Stokes for 56 on day one of the first Test on Thursday.
He has accumulated four demerit points under the International Cricket Council's (ICC) code of conduct.
The second Test at Trent Bridge starts on 14 July.
Rabada received one demerit point and was fined 15% of his match fee.
Rabada, whose comments were audible on the stump microphone, took 3-123 as England made 458 in their first innings, before reducing South Africa to 214-5 on Friday.
Players who accumulate four demerit points in a two-year period receive two suspension points, meaning they automatically miss one Test, two one-day internationals or two Twenty20s, whichever comes first.
He received three demerit points after he made contact with Niroshan Dickwella during a one-day international against Sri Lanka in February.
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Rabada, playing his 18th Test, is seventh in the ICC Test bowling rankings, having taken 74 wickets at an average of 24.39.
Fellow pace bowler Chris Morris would be the most likely candidate to replace him in the second match of the four-Test series.
However, Rabada's absence presents further problems for a South Africa side already without batsman AB de Villiers and pace bowler Dale Steyn and with captain Faf du Plessis at home after the birth of his child.
South Africa pace bowler Kagiso Rabada has been suspended for the second Test against England following an altercation with Ben Stokes at Lord's.