Financial Fraud Action UK (FFA UK) said there had been a particular rise in the scam in the last few weeks.
Several small or medium-sized companies in the UK have lost sums of between Â£10,000 and Â£20,000 as a result.
Typically, staff in a firm's finance department receive an email, which they believe is from a senior manager.
The fraudsters use special software to make the message appear genuine.
The emails request that urgent payments are made outside normal procedures, often for a pressing reason, such as the need to secure a contract.
The scam has been dubbed "whaling" fraud, as it targets the so-called big fish of business.
When the money is transferred, it goes into an account set up by the fraudsters.
"While an urgent request from the boss might naturally prompt a swift response, it should in fact be a warning sign of a potential scam," said Katy Worobec, director of FFA UK.
Staff are being advised to:
Office staff are being warned about fake emails that appear to come from one of their bosses, telling them to transfer money.