Amla, 36, was forced to retire hurt after being struck on the helmet by a short delivery from fast bowler Jofra Archer in the fourth over of Thursday’s opening match against hosts England at The Oval.
He returned to bat briefly later before South Africa were beaten by 104 runs.
"Hashim hasn't fully recovered from the blow sustained to the helmet during the match against England on Thursday and is not available for selection for the match today," South Africa team manager Mohammed Moosajee said in a statement on Sunday.
"With the quick turnaround between the two matches, he is being rested as a precaution, based on our post-match re-assessment.
"We are hopeful that he will make a full recovery to be available for selection for our next match against India.”
David Miller took his place in the line-up for Sunday's second game of the tournament for South Africa, which is also at The Oval.
South Africa take on India at Southampton on Wednesday.
(Reporting by Mark Gleeson; Editing by Sudipto Ganguly)
