Gardaí say they have seen a noticeable increase in cyber-criminals using "phishing" to steal money from people's bank accounts.
Since January, up to 250 people have reported to gardaí that they have been victims of the crime.
The amounts stolen vary from €100 to €40,000.
Gardaí advise that bank customers should not open phishing emails, as they may contain a Trojan virus that will be downloaded to their computer.
If they do open one of these emails, they should contact their bank immediately.
They should also never respond to the phishing email under any circumstance.
Bank customers should also ensure their anti-virus software is up to date.
The Garda National Bureau of Fraud Investigation has said the thefts are being carried out by criminal cyber gangs over the web from various jurisdictions.
Some are using so called "mule" accounts in Ireland to transfer the stolen money into.
This can involve the gang paying unscrupulous individuals in Ireland small amounts of money for the use of their accounts, or the gangs themselves setting up their own Irish-based accounts.
Either way, money is transferred out of the victim's account, into the mule's account, before being withdrawn locally in Ireland and sent to the crime gangs abroad.
Gardaí say the gangs are based in a variety of locations, including West Africa and Eastern Europe.
However, using remote hosting technology, they can make the phishing emails appear to come from entirely different jurisdictions to the one they are living in.
Gardaí say in many cases banks refund the money that has been stolen.
However, this is not always the case, particularly in circumstances where the individual who has been defrauded has been warned about the dangers.
The Irish Payment Services Organisation has also noticed a spike in phishing crimes.
However, it says that a number of banks in Britain are now refusing to refund money stolen using this technique, because they claim they provide enough warning information to their customers.