Share prices had risen before Thursday's opening, putting the stock on pace to rise above $46 a share for the first time in three weeks. However, after markets opened, they reversed course, dropping 1.7 percent.
The scandal became public on Sept. 8, when Wells Fargo agreed to settle with regulators for $185 million for opening about 2 million accounts for bank customers who had never asked for them.
Stumpf announced his retirement on Wednesday, effective immediately.
"While I have been deeply committed and focused on managing the Company through this period, I have decided it is best for the Company that I step aside," Stumpf said in a statement.
Wells Fargo's board of directors elected President and Chief Operating Officer Tim Sloan to succeed Stumpf as CEO. Lead director Stephen Sanger will serve as the board's nonexecutive chairman.
The stock is down more than 17 percent this year.