At least at the state level, states' general police powers have usually been interpreted to give pretty broad authority to enforce measures like quarantines and mandatory isolation if necessary to protect public health. There's a bit of recent case law from the 2014 Ebola quarantines: a few nurses who had had contact with a suspected case (but had no symptoms) were put under mandatory quarantine, and sued for unlawful detention, but courts upheld the quarantine.

There's some limit to these powers, e.g. a quarantine in SF in the year 1900 was struck down as being racially discriminatory in a way not justified by public health (only ethnic Chinese were quarantined). But courts are reluctant to second-guess this kind of thing unless it seems like a pretext.