The creature's odyssey, which was broadcast live on national television, saw officers in hot pursuit as they tried - in vain - to recapture it alive.
After unsuccessfully attempting to corral the stripy animal, vets shot it with a tranquiliser dart - only to watch as it plunged into a small lake on the golf course.
"It collapsed in the pond, so we hurriedly pulled it ashore, but its heart had already stopped beating," said Takahiro Taniguchi, a police spokesman in central Gifu.
"Veterinarians performed cardiac massage," he said, but it was not enough to prevent the "bitter aftertaste" of the animal's demise.
The zebra had bolted on Tuesday from the Mikuni West Farm in neighbouring Aichi.
The failed attempt to recapture the creature came just a month after a Tokyo zoo held a drill practising this very eventuality.
Every year, a zookeeper dresses as an animal and stages an escape, giving colleagues the opportunity to hone their techniques.
This year's creature was a zebra, which was successfully collared and returned to its pen.
But as if to prove that practice doesn't always make perfect, this week's real life response didn't quite go to plan.
According to Ueno Zoo, which staged the zebra escape drill last month, the animals are easily panicked.
Japan has previously had more success with animal escapes.
In 2012 a penguin on the run from a Tokyo aquarium outwitted authorities for 82 days before being caught.
There were more than 30 sightings of the 60-centimetre (two-foot) bird, known only as Penguin 337, who was spotted around various locations, including swimming in Tokyo Bay. - AFP