The program they are alleged to have used made victims believe their web browsing habits were being investigated by police.
The program stopped a PC working and displayed a warning message purportedly from the Metropolitan Police.
The message claimed illegal web use had been detected and demanded payment of a Â£100 fine.
The warning page used logos from both the Metropolitan Police and the Police Central Crime e-Crime Unit (PCEU) to make it look more like an official warning notice.
"I remind all computer users that police do not use such a method to impose or enforce fines, so if you are confronted by such a page do not enter any of your details," said Det Insp Jason Tunn from the PCEU in a statement.
Instead of responding, said Det Insp Tunn, people should contact the police.
All three suspects, two men and a woman, are from Stoke-on-Trent and are accused of using the malicious code to defraud victims. All three are being held in custody at a Staffordshire police station.
So-called ransomware is becoming increasingly popular with cybercriminals and more usually works by preventing a computer starting up or encrypting important documents. People often fall victim by following a link to a booby-trapped website that installs the malicious program when they visit.
Earlier this month an Australian medical centre was hit by ransomware which encrypted patient records. The malicious hackers behind the program demanded 4,000 Australian dollars (Â£2,610) to release the records.
Three Britons have been arrested on suspicion of distributing malicious software known as "ransomware".