Virender Sehwag will take over the captaincy for the matches in Port Elizabeth on Wednesday and in Centurion on Sunday, Indian media manager Rajan Nair told reporters on Monday.
Dravid sustained the injury while fielding in the slips in the third one-day international in Cape Town on Sunday.
Nair said team management was awaiting confirmation of whether Dravid's finger was fractured, or whether he had damaged ligaments.
Nair would not say whether the injury would keep him out of the test series that follows the one-day matches.
The first of India's three tests in South Africa will be played in Johannesburg from Dec. 15 to 19. South Africa hold an unbeatable 2-0 lead in the one-day series.
VVS Laxman will replace Rahul Dravid, according to the sources.