Anderson, his country's leading wicket-taker, complained of stiffness in his calf and bowled just five overs on tour so far in the first warm-up game in Potchefstroom a week ago.
The 33-year-old did not play in the second warm-up match in Pietermaritzburg which England won convincingly on Tuesday.
"@jimmy9 ruled out of the first Test vs @OfficialCSA with a calf strain. He'll be assessed for 2nd Test," the England and Wales Cricket Board said on their official Twitter feed.
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Anderson has claimed 426 test wickets during his career and overtook previous record-holder Ian Botham during England's tour of the Caribbean earlier this year.
England will start their four-test series against South Africa in Durban on Saturday with the second test at Newlands, Cape Town from Jan. 2.
(Writing by Sudipto Ganguly in Mumbai; Editing by John O'Brien)
