Bergen County Executive Jim Tedesco said Tuesday that the first case was discovered a day earlier at the Bergen County Jail.
The county sheriff's office says five inmates have been diagnosed by their symptoms. They are awaiting tests to confirm.
The quarantine means no new inmates will be accepted for at least 25 days.
Those at the jail who need a vaccination will receive one.
Mumps can spread quickly through coughing and sneezing. Symptoms include swollen glands, fever, headache and muscle aches.
Earlier this year, thousands of people at immigration detention centers in Louisiana and Colorado who were exposed to mumps were quarantined.
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