The bank announced that John Zutt, a Dutch national who has worked at the bank as a senior adviser and a lawyer, would temporarily replace Folsom until a permanent director was appointed.
Folsom's appointment to the World Bank had been questioned by colleagues due to her political ties to the Republican party and her department's pursuit of an anti-corruption campaign initiated by Paul Wolfowitz, the former World Bank president.
Robert Zoellick, World Bank president, who replaced Wolfowitz in November, said in September 2007 that he planned to keep Folsom as head of her department.
Bank insiders told the New York Times that relations between Zoellick and Folsom, which were positive in the beginning, had frayed in recent weeks.
This happened especially after editorials in The Wall Street Journal cited internal investigations and suggested that Folsom was being undercut and driven out.
The bank was recommended to examine the role of Folsom's department by a panel led by Paul Volcker, a former US Federal Reserve chairman.
"I want to make it clear that she (Folsom) was not fired, she was not forced out. She has a very good offer from the private sector and she chose to take it"
Marwan Muasher, World Bank spokesman
Muasher said on Wednesday that an internal working group reviewing the panel's recommendations had completed its report.
The bank's board would consider it next week.
Asked whether Folsom's resignation was tied to internal work currently under way to examine the role of the integrity department, Muasher told the Reuters news agency: "Not at all. When she expressed her wish to leave, the president asked her and she agreed to stay on until the review is completed."
Muasher said Zoellick offered her a different job at the bank and then asked her to stay until the bank completed its investigation of corruption in India.
The report on India was released on Friday, and it found extensive corruption in several Indian lending programmes.
The report was filled with pictures of shoddy construction work at hospitals, clinics and other facilities that had been certified as adequate.
It also contained pledges by India to work with the bank on improving its procedures, but some officials in the bank said these were similar to ones made and not kept in the past.