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:

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Seventeen-time Grand Slam champion Roger Federer did not face a single break point as he beat Frenchman Gasquet 6-3 6-3 6-1 in just 87 minutes.
Wawrinka made almost as short work of Andy Murray's conqueror Kevin Anderson, beating the South African 6-4 6-4 6-0.
Top seed Novak Djokovic will face holder Marin Cilic in the other semi.
Federer has won 16 of his 19 meetings with compatriot Wawrinka, but lost the most recent in this year's French Open quarter-finals and found his wife's courtside conduct called into question after a bad-tempered encounter at last year's World Tour Finals in London.
However, he said he was relishing the chance to meet his friend and Davis Cup team-mate in the last four.
"Stan played a wonderful match against me in Paris," he said.
"He can consistently bring the power on forehand, backhand, and serve out almost anybody when he gets hot.
"It is cool for us to have two Swiss in the semi-finals."
Anderson's win over Murray in the previous round was built on relentless aggression off the ground as well as his powerful serve, but he could not replicate those tactics against Wawrinka.
Anderson hit less than half the number of aces and less than a third of the number of winners that he managed against Murray.
By contrast, Wawrinka put together his most impressive performance of the tournament after making relatively heavy weather of beating Albert Ramos-Vinolas and Hyeon Chung in the opening rounds.
"Stan didn't make it easy," Anderson said.
"He was taking time away from me. He was swinging out and I was just a step slow."
While Wawrinka said his relationship with Federer off the court was still good, he added his countryman's demeanour on court had been changed by their increasingly competitive meetings.
"Before it was only me," Wawrinka said. "I was nervous because I knew I wasn't at his level, for sure.
"Now I think we can see that he was also nervous every time we play each other the past few years. That's a big difference, because that shows how much he knows that I can play at his level."
"Seeing all those big serves coming down meant I felt I had more time. " Roger Federer says everything seems easier on return when compared to playing John Isner in the last round.
"I needed a shirt change after the fifth game the other night. Don't think Roger changed his shirt all match." John Isner returns the compliment on Twitter.
"Hopefully nine to 10 hours." As well as clocking up time on the practice court, Federer advocates getting some serious sleeping done to reach the top.

Worcestershire Parkway station has been proposed close to junction 7 of the M5.
The government has set aside a total of £20m to pay for 75% of the cost of either building or renovating stations in England and Wales.
The county council has until 25 February to submit its bid for the fund, which is managed by Network Rail.
The Conservative-led authority has said it wants Worcestershire Parkway completed by summer 2016 if it is given money from the New Stations Fund.
The plans form part of the Worcester Transport Strategy, which requires £200m of investment.
Office staff are being warned about fake emails that appear to come from one of their bosses, telling them to transfer money.
[NEXT_CONCEPT]
Roger Federer and Stan Wawrinka will meet in an all-Swiss semi-final at the US Open after impressive wins over Richard Gasquet and Kevin Anderson.
[NEXT_CONCEPT]
Worcestershire County Council is to bid for £7m of government money to go towards the construction of a third railway station in Worcester.