Associated Press/Carolyn Kaster
In this Aug. 15, 2016 file photo, Democratic presidential candidate Hillary Clinton speaks in Scranton, Pa.
In the letter published on her website, the Democratic presidential candidate said she was "deeply disturbed" by the news, and said the bank owes all its customers a clear explanation.
Earlier in September, the Consumer Financial Protection Bureau, the Office of the Comptroller of the Currency, and the Los Angeles prosecutor accused Wells Fargo of opening accounts and collecting fees in customers' names without their knowledge or consent.
The bank opened up to two million deposit and credit card accounts, according to the CFPB.
"There is simply no place for this kind of outrageous behavior in America," Clinton said.
Wells Fargo CEO John Stumpf will testify in Congress on Tuesday.
"Even after Americans spent years working hard to recover from the Great Recession, the culture of misconduct and recklessness that preceded that crisis too often persists," Clinton said.
Clinton said she would stop plans by "Donald Trump, the Republican party, and Wall Street lobbyists" to get rid of the CFPB. In an interview with Reuters in May, Trump said he would dismantle Dodd-Frank regulations because they made it harder for banks to grant loans.
Clinton also slammed the $125 million payout to Wells Fargo executive Carrie Tolstedt when she retires at the end of the year.
Tolstedt oversaw the community banking division. Its responsibilities included the retail banking and credit card operations, which was implicated in the improperly opened accounts.
Tolstedt announced the move in July, before news of the fraudulent accounts was public.
"It's hard to imagine that top executives were unaware of a problem that involved thousands of the firm's employees," Clinton said, adding that compensation should take a hit if companies pay huge fines.