Checks revealed he had a compound fracture on his left leg, possible after it was caught in a trap.
Mr Webb said the bird could not be saved as infection had already set in the injured leg which would have damaged his kidney or liver.
"It's the worst part of our job to put down a bird which is a national icon due to human error. It's very hard to get the message through to people setting traps on the ground that it can kill a kiwi."
He said the problem was a lot of people not familiar with old-style traps went into forests to catch possums but don't realise or know these traps, which they can get cheaply, can catch kiwis as well.
"We are trying to educate new hunters and trappers to try and set traps off the ground so kiwis don't get caught. Traps should be laid about one metre off the ground."
There were special traps that could be put on the ground that did not capture kiwis, he said.
Mr Webb said people should also realise any dog could kill a kiwi and that the animal must not be allowed to roam free.
Dead kiwis are handed over to the Department of Conservation and their feathers are removed for cloak-making.
Kiwis have a lifespan of between 40 and 50 years. The recovery centre receives about 1300 injured birds annually.