It comes as a US university predicts 180,000 US deaths from the virus by October.
New York, New Jersey and Connecticut have asked people travelling from states where virus cases are rising to go into self-isolation for 14 days.
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 2.3m cases of the virus and more than 121,000 deaths.
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."
Which states are subject to the quarantine?
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.
"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.
Which US states are seeing cases surge?
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.
Florida also reported a daily record of 5,508 new infections. It brings Florida's total number of confirmed infections to 109,014, with 3,281 deaths. In the absence of a state-wide mask requirement, several cities and towns have issued their own orders mandating masks in public.
Arizona on Wednesday reported 1,795 new infections, down from the record 3,600 new infections on Tuesday, when President Trump held a campaign rally in the city of Phoenix.
At the event Mr Trump - who was not wearing a mask - insisted that the coronavirus "plague" was "going away" and again referred to the virus as the "kung flu", which the White House denies is a racist term.
Arizona officials warn that over 80% of hospital beds are currently being used, and that the healthcare system may be overrun in the coming days or weeks.
Texas on Wednesday also reported a new record daily number of 5,551 confirmed cases, with Governor Greg Abbott warning that the state was facing a "massive outbreak" and new restrictions may be needed in some areas.
Texas has seen increasing numbers of people admitted to hospital and a children's hospital in Houston has begun admitting adult virus patients.
Texas Children's Hospital urged the public to "take responsible actions - practice appropriate social distancing, wear a mask or face covering anytime you leave your home".
Both Texas and Arizona were among those states that removed coronavirus restrictions early. Texas has temporarily revoked alcohol licences from several businesses that were breaking social distancing rules.
On Tuesday the governor of Washington state, Jay Inslee, ordered all residents to wear face masks in public after confirmed infections rose by more than a third the previous week.
"This is about saving lives. It's about reopening our businesses. And it's about showing respect and care for one another," Mr Inslee said.
Several US states and cities have instructed residents to wear face coverings.
South Carolina, Utah, Mississippi and Louisiana have also seen a surge in caseload and some governors have said they may be forced to announce new lockdown measures.
The European Union is reportedly considering banning US citizens from entering the bloc as it considers how to reopen its external borders. BBC