Lieberman was the Democratic Party's vice presidential nominee in the 2000 election, which was won by Republican George W Bush over Democrat Al Gore
Initial funding of $325 million for the project includes large donations from Germany, the United States, Saudi Arabia and the United Arab Emirates, the bank said.
"This is going to be what we hope will be a multibillion dollar fund to support women entrepreneurs," World Bank President Jim Yong Kim said.
The program will work with governments "to improve laws and regulations that are stifling women entrepreneurs," pushing financial institutions to provide equity to the companies they create, the bank said.