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.
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."
CNBC has reached out to Wells Fargo and the Fed 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.