The stock fell 3 percent on Tuesday. The shares have been pressured ever since the bank was fined $185 million for opening more than 2 million fee-generating accounts without authorization to do so.
Trader Brian Kelly said that Wells Fargo isn't a buy at this point.
"You want to be aggressive? You can short it because this is not over," Kelly said. "They're going to have congressional hearings. People are going to get hauled onto TV. It reminds me very much in that sense of what's been happening with biotech where you all of the sudden everybody piles on biotech because prices went up and we didn't like it. Same thing is happening with Wells Fargo."
Trader Guy Adami said that one question investors might raise is whether or not this behavior exists at other banks. He said that if investors are looking to get into a bank stock, U.S. Bancorp is one he likes and thinks is "beyond reproach."