OCBC has asked some of its corporate banking clients to download security software, and if they fail to comply the bank will close their accounts.
This was done to guard against potential malware attacks, the bank said.
However, the move riled some of the bank's small and medium-sized enterprise (SME) customers, who were unhappy about the way the message was conveyed.
A few of these customers took to social media to say they had received letters over the past week from OCBC, giving them 14 days' notice that their accounts would be closed as the bank "can no longer support (the) account".
Customers - who posted updates on their own social media accounts as well as on OCBC's Facebook page - said the bank did not offer an explanation for the impending account closures.
They also said they had not received any calls from the bank, and were not told what to do to keep their accounts open.
In response, an OCBC spokesman said the bank has been encouraging customers to install IBM Security Trusteer Rapport, a security software that will protect their computers from cybercrime and financial malware.
"We recently wrote to a small group of customers who had not installed this software despite our asking them to do so several times. Without the software being installed, we would have to review these customers' online transactions more closely to protect their accounts. Last month, after reviewing the risk and added handling that may be required for these accounts, we wrote to the customers to tell them that we would regretfully have to close their accounts," the bank spokesman said.
"We are really sorry that the above has caused inconvenience and anxiety. We will not close the customers' accounts if the software is installed. We have already called the customers and are now working closely with them to ensure this is done. To date, we have resolved the issue with more than half of these customers."
The move follows a government clampdown on cyber security.
The Straits Times reported earlier this month that 100,000 government computers will no longer have direct access to the Web from next May, as part of efforts to keep government e-mail systems and shared documents safe.
Civil servants will still have access to the Internet, but on separate computers dedicated to that purpose or on their personal mobile devices.
Chia Yan Min