Yes, despite state law's traditional definition of smoking
You can absolutely prohibit an employee from using this device in your workplace. While it is true that the state law banning workplace smoking defines smoking as "the burning of a lighted cigar, cigarette, pipe, or any other matter or substance which contains tobacco," the matter doesn't end there. Employers are free to impose greater restrictions on workplace conduct than is stipulated in state law. Although your employee may claim the right to smoke his e-cigarette at work, unless you can show a basis for saying no, in fact the opposite is true. You have full legal authority to ban the activity unless he can show some legal entitlement to engage in it, which he will not be able to do.
Regardless of the fact that e-cigarettes do not burn tobacco, there are valid reasons to prohibit their use. E-cigarettes are products designed to deliver nicotine or other substances to a user in the form of a vapor, and a smoke-like vapor cloud is typically emitted when the user exhales. One brand claims the "highest volume of smoke in the industry" and the product's ability to deliver "a powerful vaporized smoking experience."
The vapor from e-cigarettes has been found by the U.S. Food and Drug Administration to contain detectable levels of several known carcinogens and toxic chemicals to which users and others could potentially be exposed.
In addition, the use of e-cigarettes in the workplace could create the appearance that employees are smoking in no-smoking areas, leading others to attempt to smoke real cigarettes in those areas. And regardless of whether the vapor is physically harmful to others, it could prompt employees to claim irritation from inhaling it secondhand.
To head off potential problems, consider updating your smoking policy to address the use of e-cigarettes. For example, the U.S. Department of Transportation has interpreted current regulations to prohibit the use of e-cigarettes on airplanes but is planning to amend existing regulatory language this year to explicitly ban their use. All major U.S. carriers ban e-cigarettes.
New Jersey's recently amended Smoke-Free Air Act contains language that could be helpful in developing a similar policy: "'Smoking' means the burning of, inhaling from, exhaling from, exhaling the smoke from, or the possession of a lighted cigar, cigarette, pipe or any other matter or substance which contains tobacco or any other matter that can be smoked, or the inhaling or exhaling of smoke or vapor from an electronic smoking device."