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.
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.
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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)
