Barclays has stopped offering free Kaspersky anti-virus products to new customers following an official warning about Russian security software.
The bank emailed 290,000 online banking customers on Saturday to say the move was a "precautionary decision".
UK cyber-security chiefs are warning government departments not to use software from Russian companies for systems relating to national security.
Barclays said it treated the security of its customers "very seriously".
A spokesman for Kaspersky said it was "disappointed" that Barclays had discontinued its offer to new customers.
The National Cyber Security Centre - the UK's authority on cyber security and part of GCHQ - is writing to all government departments telling them Russian security software could be exploited by the Kremlin.
But officials stressed they were not saying members of the public or companies should stop using Kaspersky products, which are used by about 400 million people globally.
Barclays told customers it would no longer offer free Kaspersky software "following the information that's been shared in the news" - but advised people with the software already installed that they did not need to take any action.
It wrote: "The UK government has been advised... to remove any Russian products from all highly sensitive systems classified as secret or above.
"We've made the precautionary decision to no longer offer Kaspersky software to new users.
"However, there's nothing to suggest that customers need to stop using Kaspersky."
It went on: "At this stage there is no action for you to take. It's important that you continue to protect yourself with anti-virus software."
The 290,000 people who received emails from Barclays are all online banking customers, who had downloaded Kaspersky in the past decade as part of a 12-month free trial offered by the bank.
Many of these customers, who could include individuals employed by the government, could have ended their subscription once the free trial ended.
Ian Levy, the NCSC's technical director, said there was no evidence the guidance to government departments should apply to the wider public.
"For example, we really don't want people doing things like ripping out Kaspersky software at large as it makes little sense," he said.
A spokesman for Barclays said: "Even though this new guidance isn't directed at members of the public, we have taken the decision to withdraw the offer of Kaspersky software from our customer website."