The battery-powered cigarettes, which can cost up to £30, do not create any smell and some doctors believe they can help smokers quit.
But Standard Life, which employs 5,500 people in Edinburgh, has said users will have to go outside to get their fix like regular cigarette smokers.
The financial services giant defended the rule saying it has had a no smoking policy for two decades and was not going to make an exception for the devices.
But doctors have criticised the firm for the hardline approach, whilst smoking groups branded the move as “utterly crazy”.
Professor John Britton, chairman of the Royal College of Physicians Tobacco Advisory Group, said that e-cigarettes had the potential to save millions of lives. He said: “The likelihood is that smoking electronic cigarettes is better than smoking tobacco.
“Electronic cigarettes have the potential to save lives. The concept of nicotine replacement is powerful and good.”
Pro-smoking organisation Forest said: “It is utterly crazy. A lot of smokers use them to help them to cut down on smoking, or to try to quit.
“If companies don’t want them to go outside for extended periods then allowing them to smoke an electronic cigarette at their desk seems logical.
“It is completely ridiculous to ban them. If it’s because they look from a distance like cigarettes then they are basically treating workers like children.”
E-cigarettes use replaceable nicotine solution cartridges which contain up to 16mg of nicotine. On inhalation the cartridge is heated and a fine mist is produced which is then absorbed into the lungs.
However, Sheila Duffy, chief executive of anti-tobacco charity ASH Scotland said she supported Standard Life’s decision.
She said: “If a company wants to ban e-cigarettes in their offices that could help avoid the impression that smoking is normal or desirable thing.
“Tobacco is not a normal product – it kills half of its consumers if used as intended. E-cigarettes are much less harmful than normal cigarettes, however there is still a lot of research to be done both on their safety and on their effectiveness.”
A Standard Life spokesman said the company introduced a policy on e-cigarettes last year.
“Standard Life has been a non-smoking company for over 20 years and we have no plans to introduce e-cigarettes.
“We encourage and support staff if they decide to stop smoking through our occupational health department and the availability of on-site smoking cessation classes.”