New Jersey's Phil Murphy said people in the three states had been "through hell and back" and did not want "another round" of virus infections.
Some southern and western states have been reporting record numbers of cases.
The University of Washington predicts 180,000 US deaths by October - or 146,000 if 95% of Americans wear masks.
So far, the US has recorded more than 2.3 million cases of the virus and more than 121,000 deaths.
Health officials say the coming weeks will be crucial to stem the outbreaks.
Currently, those states are Alabama, Arkansas, Arizona, Florida, North Carolina, South Carolina, Texas and Utah, the governor of New York state Andrew Cuomo told reporters.
People coming from those states - including returning New York, New Jersey and Connecticut residents - will be asked to quarantine upon arrival for 14 days.
Anyone found breaking the quarantine could face fines of $1,000 (£800) rising to $5,000 for repeated violations, Mr Cuomo said. He added that US states would be added or taken off the quarantine list depending on the number of new cases per 100,00 people or the rate of positive tests.