The 84-year-old man was walking in Latimer Walk, in the direction of Waitrose, at around 3pm on Sunday, March 13, when he was tapped on the shoulder by a woman.
She told him he had dropped £10, and he got out his wallet to check. The woman then went on her way.
Later he realised his card had been taken and used to withdraw £1,800 from various cash machines.
The woman is described as white, aged 35 to 45, around 5ft 2ins tall and slim. She had unkempt hair, dirty fingernails and wore dark clothing.
Officers have been conducting extra patrols in Romsey town centre and have distributed posters, with crime prevention advice.
Being aware who is around you when you use a cash machine, and to always shield your PIN
Being vigilant and wary when strangers approach you
Keeping wallets and purses close to you and to not be distracted into taking them out in front of strangers
Being wary of strangers who say that you have dropped some money or who ask you for directions
Never giving money to strangers, even in exchange for an offer.
Anyone with information on this incident, or who has experienced something similar, is asked to contact Romsey police station on 101, quoting 44160102690. In an emergency, please call 999.
Alternatively, people can call Crimestoppers on 0800 555 111, where information can be left anonymously.