The customers would be reported to Sri Lanka Central Bank and "actions will be taken to terminate the banking relationship with the offender," the banks said in a statement.
The Sri Lanka Bank's Association said they were acting on rules issued by the central bank and Sri Lanka financial transactions reporting law, where offences against children were listed.
In Sri Lanka all types of pornography as well as gambling is illegal.
A campaign to discourage child pornography use would be launched by the banks next Monday. .