The mine "spilled approximately 40,000 cubic meters (1.4 million cubic feet) of leached copper into the Bacanuchi River, a tributary of the Sonora River," the National Water Commission (Conagua) said in a statement.
The restrictions affect seven municipalities, fed by the 420-kilometer (260-mile) river, including the Sonora state capital, Hermosillo, which is home to nearly 800,000 people.
Local media broadcast pictures of orange water, which reports said had killed fish and cattle, and is affecting milk production.
Authorities are continuing their search for waste contamination and are preparing for possible legal proceedings against the mine.
Sonora state, which accounts for 27 percent of all Mexican mining, is the country's leading producer of gold, copper, graphite and a number of other mined products.
In August last year, a trailer-truck carrying cyanide for a Sonora gold and sliver mine overturned, contaminating the Yaqui River. This caused a shortage of drinking water, human illness and the death of reptiles and birds.