Arizona's Department of Health recommended that any unvaccinated child or adult who had been in contact with infected people to spend 21 days in isolation at home to curb the risk of spreading the virus.
Anyone deemed at risk of infection has been offered doses of immune globulin, which would not prevent them from getting measles but can reduce symptoms if administered within six days, authorities said.
Complications from measles can include blindness, hearing loss, pneumonia and death. One to two children of every 1,000 infected with measles will die from it, according to the US Centers for Disease Control and Prevention.
"This is a critical point in this outbreak," Arizona Department of Health Services Director Will Humble said in a statement.
"If the public health system and medical community are able to identify every single susceptible case and get them into isolation, we have a chance of stopping this outbreak here."
Humble said more than 1,000 people were believed to have come into some contact with seven measles cases confirmed in Arizona so far.
The Arizona warnings come as the state's capital Phoenix welcomes visitors for this weekend's finale to the American football season, the Super Bowl, between the Seattle Seahawks and New England Patriots.
Sunday's showpiece -- the biggest event on the American sporting calendar -- is the climax of a week-long jamboree whose epicenter is a swathe of downtown Phoenix dubbed Super Bowl Central featuring exhibits, beer gardens, free concerts and nightly firework shows.
Local media reports estimate that a million visitors, many of them from out of state, will throng the complex of attractions during Super Bowl week.
Eradication means measles is no longer native to the United States, but there were 644 cases of the disease in the US last year -- a big jump from 173 cases in 2013.
The spike coincides with an anti-vaccination trend that has emerged in recent years, particularly in North America.
Opponents fear the MMR (measles, mumps, rubella) vaccine causes autism, even though an array of studies have ruled out any link.
The latest outbreak has centered around the Disneyland theme park in Anaheim outside Los Angeles.
Four of the patients diagnosed in Arizona are members of one unvaccinated family who visited the California resort.
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