In a letter sent Monday to Federal Reserve Chair Janet Yellen, the Massachusetts Democrat said the scandal has "revealed severe problems with the bank's risk management practices." Warren said the central bank has the authority under federal statute to remove the members who were on the board as the matter transpired.
"We have received the letter and plan to respond," a Fed spokesman told CNBC.
In an agreement with multiple authorities last September, Wells agreed to pay a $185 million fine in conjunction with a scandal in which some 2 million client accounts were created without the customers' knowledge.
More accounts may be involved, according to subsequent allegations.
Even after paying the fine, Wells has continued to undergo reputational damage amid congressional inquiries and additional disclosures
Warren, who has been a harsh critic, pointed out in the letter multiple instances where she believes the board at Wells failed customers.
"The fake accounts scandal cost Wells Fargo customers millions of dollars in unauthorized fees and damaged many of their credit scores," the senator wrote. "The scandal also revealed severe problems with the bank's risk management practices — problems that justify the Federal Reserve's removal of all responsible Board members."
Wells Fargo did not respond to a request for comment. Wells Fargo shares gained about 1.1 percent in early trading, about in line with the sector.
Warren did not limit her criticism to Wells — she also said the Fed "has done nothing to date" to punish the bank "despite its ample statutory authority."
"I urge you to use the tools Congress has given you to remove the responsible board members and protect the continued safety and soundness of one of the country's largest banks," she wrote.
The scandal arose as bank employees sought to meet aggressive sales demands. Employees would enroll customers in various programs without their consent in order to make quotas that have since been disbanded.
Some 5,300 employees have been terminated as a result, and the bank also has a new CEO, Timothy J. Sloan, who took over for John Stumpf.
For the Fed to act, it would need to establish that any individual board member's actions were unsafe or unsound to the bank. The Fed likely would need to initiate an enforcement action and prove its case.
Yellen told Congress during testimony shortly after the scandal broke in September that the Fed is reviewing all operations for large banks and believes that in cases of wrongdoing, "senior management (should) be held accountable."