His place in the 15-man squad is to be taken by the uncapped 27-year-old batsman Ambati Rayudu.
Vice-captain Virat Kohli, who led the team on the field in Dhoni's absence against the West Indies, takes over as captain for the remainder of the series.
India face Sri Lanka on Tuesday in Kingston with both teams looking for their first points after each lost to the hosts in their respective opening fixtures.
Following that encounter, the tournament shifts to the Queen's Park Oval in Port of Spain, Trinidad, for the remaining three preliminary matches at the final, starting with India against the West Indies on Friday.