The pair were arrested after they tried to withdraw large sums of money that had been wired to their accounts with a Sri Lankan bank branch in the capital Colombo, the official said.
"We are looking at some USD 1.3 million that had come into three accounts in Sri Lanka," the official involved with the investigation told AFP, asking not to be named.
"We have taken two people into custody and we are looking for one more person."
Police in Sri Lanka did not disclose the name of the affected bank in Taiwan or the sum said to have been stolen, but a Sri Lankan media report said tens of millions of dollars had been wired out of the island.
In Taipei the Financial Regulatory Commission confirmed that the local Far Eastern International Bank's SWIFT system had been hacked through a computer virus but gave no details.
Taiwanese media quoted the bank as saying that it detected irregularities in its SWIFT system and there were suspicious transactions starting Thursday to Sri Lanka, Cambodia and the United States.
However, Taiwan police have recovered most of the money with the help of counterparts in other countries, the reports said.
Bank officials were not immediately available for comment.
Sri Lankan police investigated a similar theft in February last year when hackers broke into the computer system of the Bangladesh central bank and transferred USD 20 million of stolen money to a Sri Lankan businesswoman.
The money was recovered and an court investigation is pending.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)