The Pakistan-born leg spinner, who made his international debut during the World Cup, is currently second on the list of highest wicket-takers, with 11 victims from three matches.
The streaked-hair bowler, who became eligible to play for South Africa after gaining his citizenship in January, injured himself during Sunday's six-run loss against England.
"Imran injured himself during the game against England while attempting the caught and bowled, which dismissed Jonathan Trott," team manager Mohammed Moosajee said in a statement.
"The x-ray that was done today revealed a small undisplaced fracture in his left thumb. His thumb has been splintered and immobilised and a decision on what happens further will be made in the next two days."
The 31-year-old had brought up his best bowling figures of 4-38 in the same match.
South Africa play India on Saturday at the VCA Stadium in Nagpur in a Group B match.
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