The Wimbledon champion bought Cromlix, three miles from his home town of Dunblane in central Scotland, in February last year.
Campaign group People for the Ethical Treatment of Animals (Peta) sent a letter to Murray complaining that his hotel promoted hunting as a possible activity for guests.
Kirsty Henderson, campaign co-ordinator for Peta, wrote: "The idea of hunting cats and dogs, such as your beloved Maggie May and Rusty, would rightly make most of us sick, and yet the animals listed on the Cromlix website, alongside the best times of year to kill them, have exactly the same capacity to feel pain and suffer."
She added: "Will you please extend your compassion to the beautiful and sensitive wild animals who live in the vicinity of the Cromlix Hotel by refusing to promote killing as an activity to guests of your establishment?"
A spokesman for Murray's management company, 77, said references to hunting were removed from the Cromlix website earlier this month and the activity was never offered on the hotel's grounds.
The British number one was praised by Peta last year when it was revealed the menu at the hotel would be foie gras-free.
Cromlix has been extensively refurbished and reopened in April, shortly before being named Scottish hotel of the year.
The Victorian mansion features 10 bedrooms and five suites which overlook manicured grounds and tennis courts.
The hotel is being managed for the British number one by Inverlochy Castle Management International and is already fully booked for the Ryder Cup, which is being staged a short drive away at Gleneagles later this year.