City officials proposed the ordinance after Jonathan Fielding, director of the Los Angeles County Department of Public Health, said e-cigarettes threatened to make smoking socially acceptable after years of public opinion campaigns to discourage the habit.
Young people who get hooked on the nicotine in e-cigarettes may then turn to tobacco use, he said.
"We don't want to risk e-cigarettes undermining a half century of successful tobacco control," he said.
One exception to the proposed e-cigarettes ban would be "vaping lounges," businesses that allow customers to try various e-cigarette liquids. Those liquids, which typically include nicotine and flavorings, are heated in an e-cigarette until they vaporize and can be inhaled.