SYDNEY—The chief executive of Optus, the Australian subsidiary of Singapore Telecommunications, resigned following a network outage in which millions of customers including hospitals and government departments lost services for several hours.

Singtel on Monday said that Kelly Bayer Rosmarin would be replaced on an interim basis by the company’s chief financial officer, Michael Ventner. Former Optus business MD Peter Kaliaropoulos will take up the new role of chief operating officer, it added.