Stumpf retired on Wednesday amid questions about the bank's sales practices, which resulted in $185 million in penalties. Last month, Warren grilled the then-CEO, accusing him of "gutless leadership" and failing to hold himself accountable for his staff's actions.
Warren tweeted on Wednesday that she would still like to see Stumpf "return every nickel he made" during the period the fake accounts were opened, as well as face an investigation by the Department of Justice and Securities and Exchange Commission.
Stumpf previously denied that the practice of cross-selling — offering existing customers other products — was a scam and said it is "a way of deepening relationships."
A spokesman for Wells Fargo said that Stumpf would not receive severance pay when he departed the company.
"There are some retirement benefits that are detailed in our proxy statement. They are not accessible for the next six months. That is a normal lag time," the spokesman said in a statement.
Warren renewed her assertion that Stumpf should be criminally investigated. She has previously said that change would only come to Wall Street if executives faced a real threat of jail time.
When Stumpf testified on Capitol Hill, Warren slammed him for not being accountable while former employees were "squeezed to the breaking point so they would cheat customers."
Wells Fargo declined to comment on Wednesday on Warren's tweets.