In Los Angeles, where residents use an average of 265 litres of water a day, an academic study found that the most affluent neighbourhoods used up to three times more than others.
In wealthy southern cities such as Malibu and Newport Beach, where people have large front lawns, daily consumption was more than 560 litres a person in January.
The director of the California Centre for Sustainable Communities, Stephanie Pincetl, told the Los Angeles Times: "The problem lies, in part, in the social isolation of the rich, the moral isolation of the rich."
The rich, she said, were "lacking a sense that we are all in this together".
Last year was the warmest on record in California, which is in the middle of its driest spell for centuries. Scientists warn that the region may be entering a "mega-drought" lasting decades or more.
Until now, most California cities have chosen not to punish people for excessive water use, but simply to raise awareness.
Beverly Hills, for example, sought to reduce consumption by 10 per cent by encouraging residents to curb their watering and use recycled water in their decorative fountains.
But in Santa Cruz, heavy water users can be fined hundreds of dollars and sent to "water school" to change their habits. The city reduced its water use by 25 per cent last year.
Brown's 31-point plan calls for golf courses and other landscaped areas to reduce water use, and bans watering of roadside verges.
It includes schemes and incentives to replace more than 4 million square metres of lawn with drought-tolerant landscaping.
"The great myth of California water is that someone else is always responsible," said Jon Christensen, of the University of California's Institute of the Environment and Sustainability.
"There are longstanding divisions between rural agriculture and urban areas, between northern and southern California.
"What I haven't seen before is this sharp focus on the wealthy, but it still fits the overall pattern - the first thing Californians do in a drought is find somebody else to blame.
"But we're all in this together, and focusing on one type of water user is not going to solve the problem."
While battle lines are being drawn between rich and poor, a bigger conflict is brewing between town and country.
Ninety-five per cent of Californians live in urban areas, and they use only 20 per cent of the state's water.
But the governor's restrictions do not apply to agriculture, which uses the remaining 80 per cent.
Farmers say they already face dramatic cutbacks because of the drought.
California's agricultural industry, which produces almost half the fruits, vegetables and nuts grown in the United States, left 202,350ha fallow last year, losing about US$1.5 billion ($2 billion).
Last year and again this year, the federally-run Central Valley Project, which oversees the irrigation canals that run through the state's agricultural heartland, allocated farmers a zero per cent share of the water they carry.
