AUTHORITIES have been forced to euthanaise a female eastern grey kangaroo which had been shot through the top of the leg with an arrow.

The NSW Wildlife Information Rescue and Education Service have dug into their own pockets to offer a $200 reward to anyone with information that leads to a prosecution over the senseless act of animal cruelty.

The kangaroo's injury was first reported on Sunday when it was spotted at the golf course in South Grafton, but police and WIRES but couldn't get close enough to put the animal out of its misery until three days later.

Clarence Valley WIRES chair Patricia Edwards said the kangaroo was a healthy young female in the peak of condition when she was shot, which was probably the only reason she managed to hang on in agony for four days.

National Parks and Wildlife Services Clarence South Area Manager Andrew Lugg said it was unfortunate that the animal had to be put down.

"This animal would have inevitably died a slow and painful death," Mr Lugg said.

"This is the second animal we are aware of in the area where kangaroos have been shot and wounded with arrows since Christmas."

Clarence Valley WIRES, RSPCA, Police and NPWS have also spent time searching for an eastern grey kangaroo with an arrow lodged in its body, last seen on Gunhill Drive, Woombah.

It was reported by a family at Woombah on January 7, who called to say the wounded kangaroo had laid down in their front yard.

While a search by the RSPCA failed to find it, WIRES Macropod coordinator Mairi Macleod said judging by the extent of its injuries it would most likely have already died.

"It's an absolutely horrible way to die," Ms Macleod said.

"I think it's absolutely appalling that people feel they can do this to animals just for enjoyment, if that's what it's for."

Ms Edwards has offered a cash reward for information on the South Grafton incident, and said she felt conditions should be placed on purchasing or owning a bow and arrow - the weapon she suspects was used on the kangaroo - in Australia.

Despite crossbows, sling shots and laser sights being classed as prohibited weapons in Australia, bow and arrows are not controlled as they are classified as general archery equipment.

In November, a third marsupial injury involving an arrow was reported by a Woombah man who said he accidentally shot a kangaroo through the tail.

Once again, authorities failed to locate the animal.

Penalties of up to $3300 or six months jail apply for killing kangaroos, which are a protected species.

If anyone has information concerning this matter they can phone Crime Stoppers on 1800 333 000, or the Grafton NPWS on 6641 1500.