The woman was contacted by a caller claiming to be from the Royal Bank of Scotland fraud department.
She was told there was suspicious activity on her account and advised to transfer the money to another account.
The woman was told to contact the number on her bank card, but police said the fraudsters had kept the line open, resulting in her still talking to them.
Police Scotland is investigating the fraud.
The woman, who wishes to remain anonymous, believed she was doing the right thing by dialling the number on her card. She did not know the fraudsters had been able to stay on her line.
Ch Insp Brian Mackay said: "Extremely convincing in their scamming techniques, these despicable individuals have the potential to harm any member of the community who is unfortunate enough to be targeted.
"Our advice is never engage with anyone cold calling you, especially when it relates to supposed account security.
"If you have concerns regarding financial or bank-related issues pay a visit to your local branch, who will always be happy to assist you."
A woman in Nairn has lost £26,000 to a bank scam, police have said.