Ed Lyman, the marine mammal response manager for the Hawaiian Islands Humpback Whale National Marine Sanctuary, said the rope could have killed the yearling whale because it may have interfered with its feeding over time.
The whale - believed to have been born last year - would have also grown into it if not removed.
"We saved a whale from a life-threatening entanglement," Lyman said.
During the rescue operation Sunday, officials first slowed the whale by weighing it down with buoys and a sea anchor. Then they used a specially fashioned, 24-foot-long pole to position a folding knife around the rope on the whale's back.
They attached a knife to another sea anchor and waited for the weight of the anchor to pull the knife through the rope. It came free in about 10 minutes.
"There was some uncertainty, but then all of the sudden the buoys fell still and the lines kind of spread apart and started to sink," said David Schofield, marine mammal stranding response coordinator for the Pacific Island Regional Office of the National Marine Fisheries Service. "There was jubilation. It was a really good feeling."
A whale-watching cruise spotted the entangled animal last Tuesday off Maui. The next day, about a hundred yards of the yellow, polypropylene line came free, but several hundred yards were still attached.
Officials were unable to attempt to free the whale for several days because of rough seas, but the weather was good Sunday. The rope ran through the animal's mouth, around its head and behind its blowhole.
Rescue efforts were made more difficult by the presence of two adult whales traveling with the juvenile.
The adult whales - believed to be the mother and her male escort - had mostly been swimming on either side of the young whale.