Organised gangs, thought to be based in London, have been targeting students through sites including Bebo and Facebook to pay fake cheques for large sums of money into their bank accounts, and then try to withdraw the cash almost immediately.
It is believed the students are being offered a share – a few hundred pounds at most – of the bumper cheques to carry out the fraudulent transactions.
While only a few cheques manage to get through, it is estimated that around 20,000 to 25,000 has been successfully cashed by students in the area in the last seven months.
In one of the most recent incidents, a 20-year-old male student was arrested and charged in connection with alleged forgery and fraudulent activity after entering a bank in Musselburgh on Monday and handing over a bogus cheque for more than 16,000. Bank staff alerted police and officers from Lothian and Borders Police Specialist Fraud Unit and the Serious and Organised Crime Unit are now investigating "similar transactions".
DS Colin Aitken, from the Specialist Fraud Unit, said: "The students are told that they will not get caught even though they know the activity is criminal.
"In fact, they are involved with dangerous criminals who will pursue them and demand their pound of flesh even if transactions fail."
He added: "Many of the students are foreign nationals, and if found guilty at court of fraud will have a criminal record, probably be expelled from the universities or colleges they are at, and will in all likelihood be deported."
The criminals even pay for flights for the students to travel across the UK, where they meet with the criminals before cashing cheques at different branches.
DS Aitken said: "The interesting thing is they are recruiting the students in Edinburgh but paying for them to travel to banks anywhere in the UK to cash the cheques. The students are not being duped into it, they are aware that it is illegal."
Students being targeted by crime gangs has been highlighted by police as a growing problem since around September last year.
Hundreds of students at universities and colleges throughout Edinburgh and the Lothians are thought to have been approached about cashing fake cheques, which are often for tens of thousands of pounds.
DS Aitken said: "Quite often the cheques are for just below 10,000 because that is a cut-off mark for the banks."
President of Edinburgh University Students' Association, Thomas Graham, 23, said he was not aware of the problem.
He said: "I think any issue like this where students are being exploited or taken advantage of is a worry for us."
Police are asking anyone who has been approached on the matter to contact them immediately.