A female suspect first contacted the victim in Zurich in November, posing as an officer who claimed to be investigating a network of thieves, according to the ATS news agency.
The woman was told that employees at her bank were planning to rob her.
The suspects asked the woman to keep details of their investigation secret.
They then instructed her to transfer her assets to a new account through a series of payments, in order to protect her savings from being stolen by her own bank.
A police investigation into the scam, which cost the woman 3.6 million Swiss francs, is ongoing, ATS said.