DHAKA, Bangladesh — Nobel Peace Prize laureate Muhammad Yunus took charge of Bangladesh’s caretaker government on Thursday, hoping to help heal the country that was convulsed by weeks of violence, forcing Prime Minister Sheikh Hasina to quit and flee to neighboring India.

Known as the “banker to the poor,” Yunus is the pioneer of the global microcredit movement. The Grameen Bank he founded won the 2006 Nobel Peace Prize for helping lift millions from poverty by providing tiny loans…