The 39-year-old man was arrested yesterday on suspicion of theft and fraud by misrepresentation in connection. He has since been released pending further enquiries.
Earlier this month, Humberside Police appealed for information following reports of three separate incidents in Willerby, Beverley and Cottingham.
In each case a man came to the door and claimed he had a parcel for the victim but that an outstanding postage charge needed to be paid by debit card before he could hand it over.
The culprit then claimed he could not get a good enough signal on his card machine and moved away, but instead left – taking their card with him.
The cards were then used to steal hundreds of pounds.
Detective Inspector John Symes said: “I’d like to thank everyone who’s been in touch with information – and those who have passed on our warning to their friends and family.
“I would also urge anyone who believes they have been taken in by this or similar scams to get in touch.
“There’s no need to be embarrassed and it might be that you can provide vital information that will help us bring the person responsible to justice.”
Anyone with information is asked to call 101, quoting incident number 16/78364/18.