The US bank also told employees not to provide opinions or influence voters, and "not to assume a particular result and not to engage in campaigning", according to the Financial Times.
The group has also reportedly decided not to go ahead with a planned donation to the campaign for Britain to remain in the EU.
Bank of America's European headquarters are in London, meaning the upcoming vote on the UK's EU membership could lead to big decisions for the company.
Meanwhile, research out today suggests that several firms are unprepared for the implications of a vote in favour of Britain leaving the EU. According to a poll by the Governance Institute and the Core Partnership, 47 per cent of company boards have not considered the result of the EU referendum and the effect it might have on their business.
The UK will vote on whether or not to remain a part of the EU on Thursday 23 June.
Bank of America declined to comment.