Another message said he needed a bullet if he "attacked" pitbulls again.
Garner said Mediaworks, his employer, took the issue seriously so they contacted the police who have given one of the people a warning.
"I want to thank the New Zealand Police for acting so quickly and for sorting this issue out. Everyone is entitled to their opinion but threatening to kill someone as a result is a step too far.
Following a spate of vicious dog attacks by pitbulls, Garner said on Monday he hated them and that "we must ban them".
"How many more children need to be attacked and possibly killed before someone takes decisive action. The law no longer works."
Following the death threats, Garner said he won't back down from his views or be shaken by the messages.