Danske is under investigation in the United States and several other countries for payments totalling 200 billion euros ($223 billion) through its small Estonian branch, many of which the bank said were suspicious.
For Commerzbank, the unexpected departure of Engels, its long-time chief financial officer, comes as the German bank is in the middle of a review of its strategy following this year's failed merger talks with Deutsche Bank.
Commerzbank, Germany's second-largest bank behind Deutsche, is looking at possible staff cuts and closing some branches, sources have told Reuters.
Danske Chief Executive Chris Vogelzang, who joined Denmark's largest bank on June 1, sacked former interim CEO Jesper Nielsen that month as he sought to draw a line under the money laundering scandal, which rocked investor confidence and prompted investigations around the world.
Danske also said on Thursday that Berit Behring, who oversees the bank's Swedish operations, will take over as new head of wealth management from Jacob Aarup-Andersen.
Andersen will take up the position as CFO until Engels joins the bank in April next year, and will the move to a position as head of Danish banking activities, Danske said.
The bank also said it is looking to replace Jim Ditmore, who will step down as chief operating officer.