TORONTO—BlackBerry Ltd. said three senior executives and a board member will leave the company, the first shake-up since interim Chief Executive John Chen took the helm at the smartphone maker a few weeks ago.

Chief Operating Officer Kristian Tear and Chief Marketing Officer Frank Boulben will depart immediately, BlackBerry said Monday. The Waterloo, Ontario, company also said James Yersh, who was head of compliance, will succeed Brian Bidulka as chief financial officer, though Mr. Bidulka will remain as a special adviser to...