Heavy afternoon showers caused damage to the outfield before the scheduled start of play and despite a lengthy dry spell, conditions did not improve enough for the match to proceed.
The match officials made three inspections before deciding no play was possible.
South Africa had already bagged the series with victories in the first two matches.
The teams will next play five one-day internationals before a four-test series starts next month.
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(Reporting by Sudipto Ganguly in Mumbai; Editing by Nick Said)
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