Some 70 percent of those who cast their ballots voted no to the measure, according to an official preliminary count.
A summary of the referendum said that natural resources such as water, soil and air were often used in Switzerland and abroad to such an extent "that they are unable to recover".
"The Environmental Responsibility Initiative requires that economic activities do not consume more resources and release more pollutants than is permitted for the preservation of natural resources," it said, setting a 10-year deadline.
The text did not give any details on how the shift would be implemented, such as regulations, bans or incentives, but said that "due to the short time limit, radical measures are likely to be required".
In line with earlier predictions of a solid majority against the "no" vote won in all cantons.
Leftist parties backed the proposed text that would put in the constitution an engagement not to use more natural resources than the Earth's limits.
"The aim is to achieve, within a decade, an economy and society in which the quantity of resources consumed and pollutants discharged remain in proportions that are sustainable for the environment," said Greenpeace, which backed the yes camp, in a press release.
But the government, business groups, right-wing and centre-right parties opposed the measure, arguing it would endanger economic growth.
Before the vote, the leading Swiss People's Party (SVP) called the initiative "dangerous".
"It would result in a very significant increase in prices or a decrease in the diversity of supply in varied areas such as food, housing, mobility and clothing," it said.
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