The Jewish owner of The Ivy restaurant is offering £15,000 reward for capturing the vandal who shot two stags on his estate.
Police are investigating the possibility that the attacks may have been intended to send a threatening message to Mr Caring.
Richard Caring, who also owns celebrity hotspot Annabel’s nightclub, has now hired former SAS soldiers as security guards for his estate in Exmoor.
The businessman, who is 146th on the Sunday Times Rich List and worth an estimated £360 million, called the hunter “a lunatic with a high-powered rifle”.
He said: “Poaching is one thing but killing just for enjoyment is quite another.”
“We have very serious security in place now 24 hours a day. I would love them to try again now.”
The attacks took place on the estate near Dulverton. One stag was left to die in front of Mr Caring’s house and another was found dead two weeks later.
One of the animals is believed to be worth around £2,000.