The move is a bid to "prevent the re-normalisation of smoking", Wales' Health Minister Mark Drakeford said, with e-cigarettes enjoying a surge in new users.
The administration in Cardiff said it wants to bring the devices in line with existing smoking laws, meaning people could not use e-cigarettes in pubs, restaurants and offices.
The plans are part of a new public health bill which would likely come into force in 2017 if it clears the Welsh Assembly.
"Anywhere you can't use a conventional cigarette, then you won't be able to use an e-cigarette either," said Wales' Health Minister Mark Drakeford.
"It will prevent the re-normalisation of smoking.
"We have worked so hard in Wales to try and bear down on the harm that smoking does -- and allowing e-cigarettes to be used in the way they currently are risks undoing the progress that has been made."
Wales was the first part of the United Kingdom to ban smoking in enclosed public places, in April 2007.
E-cigarettes are battery-powered cylinders that heat a nicotine-containing liquid into a vapour that is inhaled.
Some health experts are concerned about the rising popularity of the devices and fear the rapid technological development of e-cigarettes is running far ahead of scientific research into possible side-effects of "vaping".
Welsh local health boards and the British Medical Association, the professional body for doctors, support the new plans.
However, anti-smoking campaign group ASH and the Cancer Research UK charity are against.
ASH said there was "little evidence" that vapour causes the same harm as second-hand smoke.
"Electronic cigarettes have been shown to help people quit smoking and there is no evidence to currently suggest that they act as a gateway to smoking for young people in the UK," it said.
Kirsty Williams, leader of the opposition Welsh Liberal Democrats, said: "There is very little evidence to date that e-cigs emit anything more harmful than water vapour. Therefore any ban on e-cigs is completely unjustifiable."
Several European countries, including Belgium, Luxembourg, Malta, Slovenia and Lithuania, have already banned e-cigarettes in enclosed public places.
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