The injury could also sideline the 33-year-old from the first two tests against Australia next month.
It is another injury blow for the Proteas, who have already lost AB de Villiers due to a finger injury for the first three matches of the 50-over series against India.
Du Plessis fractured his right index finger in the six wicket loss to India in the opening ODI in Durban on Thursday, a match in which he scored a 120 runs to anchor the home innings.
He will be out of action for between three and six weeks, Cricket South Africa said in a statement on Friday, leaving him in a race against time to be fit for the first of four tests against Australia that start on March 1.
Farhaan Behardien has been called into the limited overs squad as a replacement, while the Proteas have also added uncapped Heinrich Klaasen as a reserve wicketkeeper-batsman.
There are five more ODIs in the series against India followed by three Twenty20 internationals.
(Reporting By Nick Said, editing by Pritha Sarkar)
