Many have been the targets of cyber attacks as a result.
This comes as a federal investigation into the WikiLeaks release of 250,000 secret U.S. documents continues.
WikiLeaks responded to Bank of America's announcement with a Twitter message urging supporters to stop doing business with the bank.
"We ask that all people who love freedom close out their accounts at Bank of America," WikiLeaks said in its posting Saturday. It also called on businesses to switch funds from the bank.
The website also promises to release documents exposing unethical banking practices.
Meanwhile, WikiLeaks founder Julian Assange said he fears that the United States is getting ready to indict him.
Assange was released on bail Thursday on condition he stays on a 600-acre estate in eastern England, wears an electronic tag and reports to police daily. Assange was in jail since Dec. 7 after he surrendered to police over a Swedish sex-crimes warrant.
The Associated Press contributed to this report.