Public Health Wales said it could potentially lead to nicotine addiction in adult life.
It recommends restrictions on advertising e-cigarettes in all media regularly viewed by children.
A vaping company said it should be able to market itself as an "alternative to smoking".
There are also calls for restrictions on the use of e-cigarettes in and around school grounds and a register of retailers to be set up to prevent their sale to under 18s.
E-cigarettes deliver nicotine within an inhalable aerosol by heating a solution that typically contains nicotine, propylene glycol and or glycerol, and are available in a variety of flavours.
Ashley Gould from Public Health Wales (PHW) said: "You can buy bubblegum, candyfloss, jam doughnut flavour e-cigarettes and they are only aimed at one audience - and that's about recruiting children."
PHW said while the health risks associated with e-cigarettes were significantly lower than cigarettes "they are not without risk."
It said the potential risks were:
The potential benefits e-cigarettes can have on smokers were also identified.
The UK's Royal College of Physicians previously said they should be offered to smokers to help them quit.
Mr Gould said for people who are smoking and want to continue to do so, they would "100% advocate making the switch to e-cigarettes because it's less harmful than continuing to smoke".
Joe Bevan, director at Celtic Vapours, said he would like to be able to market his product "as an alternative to smoking."
"We're not nicotine replacement therapy and we're not smoking," he added.
He said the vapour e-cigarettes give off is "no more dangerous than the actual air we breathe on a daily basis.
"Our emissions tests have shown if you stand by a busy road you will inhale more toxins."
Health officials are calling for a ban on the sale of confectionary-like flavours in e-cigarettes over concerns they appeal to children.