In what is the first highlighted case in the country, a local woman was enjoying a drink in Molly Malones in the city centre when she was approached by a member of staff and asked to put the e-cigarette away.
She was told the battery-powered smoking simulator - which emits a non-toxic vapour and is used by those trying to cut back - would need to be used outside the Hope Street pub which is also where smokers gather.
The Irish bar is a Belhaven pub and is managed by Suffolk-based Greene King, which confirmed that it is company policy not to allow electronic cigarettes to be used inside its premises.
The customer, who lives in the West End of the city, said she was left "speechless" and said pubs should be doing more to help those trying to quit.
The Scottish Licensed Trade Association told the Evening Times that this is the first case it has been made aware of.
But chief executive Paul Waterson, who is based in Glasgow, said he thinks more pubs may follow suit.
Mr Waterson told the Evening Times: "This is the first case anyone has been in touch with us about in Scotland but I think this is something we are going to see more and more of. Our position is that the decision on whether to allow these e-cigarettes rests with the individual publican."
He added: "The problem is that they cause confusion among other customers.
"There is a vapour which comes from the devices and they can be mistaken for real cigarettes."
He added that some landlords might take the view that they do not want to risk being wrongly reported for flouting the smoking ban.
But the aggrieved Molly Malones customer added: "There is no smell from an electronic cigarette, only vapour.
"And the one I was using didn't even look like a cigarette as it is purple and black.
"I find it completely ridiculous that the pub is banning something which helps their customers cut down and eventually stop smoking.
"Nobody is likely to go outside a pub to have a couple of drags on an electronic cigarette, so will be more likely to go outside and have the real thing.
"So much for the pub supporting people who are trying to do the right thing and stop smoking."
A spokeswoman from Belhaven said: "To avoid any confusion for staff and customers and to ensure the comfort and enjoyment of all, we do not allow e-cigarettes to be used inside our businesses."
According to the Greene King website, the company manages a further 16 pubs in the city, including the Scotia Bar in Stockwell Street, The Snaffle Bit in Sauchiehall Street, Coopers in Great Western Road and the Old Schoolhouse in Woodlands Road.