These losses are due to its $55bn of exposure to US mortgage lending to borrowers with poor credit rating histories.
Citigroup, America's largest bank, said that losses may rise if markets worsen.
Prince, 57, becomes the second prominent bank chief to resign in a week.
Stan O'Neill, the head of Merrill Lynch, resigned after reporting heavy losses.
Prince and O'Neill are the most notable casualites of the debt crisis that has also cost other financial institutions billions of dollars.
"I am responsible for the conduct of our businesses," Prince said in a memo to employees.
"The size of these charges makes stepping down the only honourable course for me to take as chief executive officer. This is what I advised the board."
Rubin said: "It was the honourable course, given the losses we are now announcing."
Prince became chief executive of Citigroup in 2003.
His leadership was noticeable for high turnover of senior executives, strategic questioning by shareholders, and rising loan and credit losses.
Shares in the bank are about 20 per cent lower than when Prince began his tenure, and have fallen 32 per cent this year.
Such issues have generated calls for the bank to be broken up because it had too many separate lines of business.
Citigroup were particularly badly hit by the third-quarter credit crunch this year due to its size, history and CEO who maintained faith in his "umbrella model" strategy for years.
Prince leaves with many investors angry with his management.
However, his supporters argue that matching the large profits Citigroup made in the 1990s was always going to be difficult.