In a statement, the company said those targeted by the scam receive a text message informing them they have won a European lottery.
The text includes an international number to contact. When this number is dialed, an Arabic automated voice response system tells the caller they will receive a "significant sum of prize money" via secure transfer.
In order to initiate the transfer, they are asked to provide details of their bank account and credit card number.
Qtel traced the calls to Liechtenstein. It said the sophistication of the operation is reflected by the 20 different number combinations the fraudsters have used to get around the company's blocks.
It is now reminding all of its customers they should never divulge bank details, credit card numbers or passwords to unknown persons via text or phone.
Fraud prevention service Cifas warned earlier this week that SMS 'smishing' scams like the one targeting Qtel customers are becoming an increasingly common tool for online fraudsters.