Ramsay has been criticised for his decision to show footage of himself and his eight-year-old son using ferrets to hunt for rabbits and for screening one of the ferret owners killing the rabbit.
Last week, Ramsay claimed that his son had accidentally pulled off a live rabbit's head during the same expedition, but this was not featured in the programme broadcast on Tuesday night.
Animal rights organisations, including Viva, have reacted angrily, claiming that it was barbaric and that Ramsay only included the footage to cause controversy and boost his own profile.
RSPCA officers have received calls from viewers expressing their concern about the episode, but the organisation said that no laws had been broken.
A spokesperson for Channel 4 said: "As part of the current series of Gordon Ramsay's 'F Word', Gordon features in a regular strand in which he sources and cooks new or unusual ingredients. Within this strand, he explored the viability of finding, hunting and eating wild rabbit, historically a widely-consumed food but no longer part of the mainstream diet.
"The location of the shoot was private land where rabbits cause extensive damage. In this context, Department for the Environment guidelines were being followed and control measures, including ferreting, were legal and in place."
The complaints follow similar protests about another Channel 4 show in which rival chef Jamie Oliver was shown slitting a lamb's throat.