The Eastern Grey kangaroo shot in the head with an arrow has been operated on and his prospects of a full recovery are good.

Melbourne Zoo vet Dr Michael Lynch, who performed the surgery to remove the arrow, said he will monitor the kangaroo for the next three weeks but is cautiously optimistic.

"This was a big injury, but because the arrow didn't seem to have been in there for a long time, and the injury was fresh, hopefully he'll be okay," Dr Lynch said.

"I'm cautiously optimistic about the kangaroo's prospects for a full recovery."

Wildlife Victoria has offered a $10,000 reward to catch the person responsible.

Wildlife Victoria media co-ordinator Fiona Corke said she couldn't believe anyone could be so cruel.