The first-term Democrat spoke about the new proposal made Monday by fellow Democrat New York Gov. Andrew Cuomo that would impose such a fine.
"New York and New Jersey do things a little bit differently," Murphy said during a radio interview on 104.3-FM. "I don't know that we will be fining people."
Speaking to "Good Morning America," Murphy said, "We'll do it our own way."
He added that he's taking it seriously because "we've been through hell."
New Jersey joined New York and Connecticut last month in advising travelers from states with outbreaks that they'll need to quarantine for two weeks upon arrival.
On Tuesday, all three moved Delaware from their lists.
During his afternoon press briefing, Carney announced Pennsylvania has also taken Delaware of its list. Philadelphia no longer shows Delaware on its list either.
"We were taken off their lists today," Delaware Governor Carney said. "The reason we've been removed from their lists is because our data meet their criteria."
In New Jersey, there are currently 22 states on the quarantine list: Alabama; Arizona; Arkansas; California; Florida; Georgia; Idaho; Iowa; Kansas; Louisiana; Minnesota; Mississippi; Nevada; New Mexico; North Carolina; Ohio; Oklahoma; South Carolina; Tennessee; Texas; Utah; and Wisconsin.
In Pennsylvania, there are currently 18 states on the list: Alabama; Arizona; Arkansas; California; Florida; Georgia; Idaho; Iowa; Kansas; Louisiana; Mississippi; Nevada; North Carolina; Oklahoma; South Carolina; Tennessee; Texas; and Utah.
The advisory includes states if their seven day rolling average of positive tests exceeds 10%, or if the number of positive cases exceeds 10 per 100,000 residents.
New York's policy says airport travelers from those states face a $2,000 fine if they leave the airport without filling out a contact tracing form. Impacted travelers could face a hearing and an order requiring mandatory quarantine, under a new state emergency health order issued Monday.
Murphy has said he lacks the constitutional authority to block travelers from coming to the state. Instead, he has called for people to be behave responsibly.
On GMA, the governor went on to say that he feels the communication and compliance by the leaders of Jersey Shore counties and townships is going very well. He called the Jersey Shore "an American jewel."
Murphy said that visits to the area are up because people are staying close and not traveling elsewhere this summer.
Although the demand to visit the beaches is higher than ever before, Murphy said, "We have to keep on top of it."
In light of the governor of California moving Los Angeles to digital learning for the fall, Governor Murphy was asked if that changed his thoughts on the fall for students in New Jersey.
"We still hope to be back to school, but we have to do it responsibly and we have to do it right. We're watching that very closely," he said.
Murphy added that his biggest concern is a student passing the coronavirus to an older educator.
Protesters took to the street outside the governor's home over the weekend to chant, "Burn your mask."
Murphy responded, "Everyone has a right to protest but we are making these decisions based on science."
"I don't like wearing the mask either, but it's the smart thing to do right now," he added.
The Associated Press contributed to this report.