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4 year oldNew 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.
On Wednesday, White House spokesman Judd Deere said the quarantine would not apply to President Trump, who has been in Arizona and is due in New Jersey at the weekend.
"The president of the United States is not a civilian. Anyone who is in close proximity to him, including staff, guests, and press, are tested for Covid-19 and confirmed to be negative," he said.
So far, the US has recorded more than 2.3 million cases of the virus and more than 121,000 deaths and health officials say the coming weeks will be crucial to stem the outbreaks.
On Tuesday America's top infectious disease expert Dr Anthony Fauci told lawmakers there was "a disturbing surge of infection" and "increased community spread" in many southern and western states.
He told Americans to take social distancing measures, saying: "Plan A, don't go in a crowd. Plan B, if you do, make sure you wear a mask."
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 100,000 people or the rate of positive tests.
"This is a smart thing to do," New Jersey's Governor Phil Murphy said.
"We have taken our people, the three of us from these three states, through hell and back, and the last thing we need to do right now is subject our folks to another round."
The state of Washington had initially been included in the list due to a data reporting error - but this was later corrected, Mr Cuomo's press secretary Caitlin Girouard said.
The overall number of infections in the US rose by a quarter last week, with 10 states reporting a rise in cases of more than 50%, according to Reuters news agency.
On Wednesday California reported a record 7,149 new confirmed cases, bringing the state's total to 190,222 cases, officials said. Governor Gavin Newsom said the state had carried out more than a million tests over the past two weeks, with about 5% coming back positive. Mr Newsom has made wearing a face mask mandatory in public.
Walt Disney said it was delaying reopening of its Disneyland Park and Disney California Adventure Park originally set for 17 July. The company said it first needed to receive approval from government officials.
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