The 35-year-old Massachusetts man who was attacked on Signal Mountain spent Sunday night in hospital after the bear bit him several times while he pretended to be dead.
There was no word when Signal Mountain or a road and trail to its 2,300-metre summit would reopen.
Such closures are typical after the handful of grizzly attacks on public land in the Yellowstone region every year.
The decision not to pursue the bears, which officials determined behaved naturally after being surprised, also was consistent with attacks that don't involve campsite raids, eating food left out by people, or similar behaviours that make bears more dangerous.
Rangers track and study many of the Yellowstone region's 1,000 or so bears but weren't familiar with the ones responsible for the attack on Sunday afternoon, according to the statement.
The attack happened even though the victim was carrying bear-repellent spray and made noise to alert bears in the forest, the statement said.
Speaking to rangers afterward, the man said he came across a small bear that ran away from him.
As he reached for his bear repellent, he saw a larger bear charging at him in his periphery vision.
He had no time to use his bear spray before falling to the ground with fingers laced behind his neck and one finger holding the spray canister.
The bear bit him several times before biting into the can of pepper spray, which burst and drove the bears away.
The man got to an area with cell phone coverage and called for help.
A helicopter, then an ambulance evacuated him to a nearby hospital.
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Investigators suspect from the man's description that the smaller bear he saw was an older cub belonging to the female grizzly that attacked.
Mother bears aggressively defend their offspring and remain with them for two to three years after birth.
Park officials didn't release the victim's name. He was expected to make a full recovery.