"Dear PETA, Chill. At least Trig didn't eat the dog," Palin posted on Facebook.
Palin, 50, posted the photos of Trig, her youngest son, who has Down's Syndrome, on New Year's Day.
"May 2015 see every stumbling block turned into a stepping stone on the path forward," Palin, who was governor of Alaska from 2006 till 2009, wrote.
Following this, People for the Ethical Treatment of Animals said in a statement on Friday that Palin had "no apparent sympathy for the dog" and that the organisation "along with everyone else, is used to the hard-hearted, seeming obliviousness of this bizarrely callous woman."
Also Read
PETA also slammed Palin, who was the running mate of Republican US Presidential nominee John McCain in 2008, after she was interviewed at an Alaska turkey farm as birds were being slaughtered in the background.
DeGeneres was PETA's person of the year in 2009.
She asked whether the organization went "as crazy when your heroic Man-of-Your-Lifetime" President Barack Obama "revealed he actually enjoyed eating dead dog meat?"
In his autobiography 'Dreams from my Father,' Obama wrote that he was "introduced to dog meat" while living in Indonesia. He wrote that it was "tough" but did not say whether or not he enjoyed eating it.
Palin also said her pets are well-cared for.
She added, "Jill is a precious part of our world. So is Trig."
Meanwhile, PETA President Ingrid Newkirk responded to Palin's latest outburst, saying, "PETA simply believes that people shouldn't step on dogs."
"Palin's Facebook response shows us that she knows PETA about as well as she knows geography."
"We have no reason to believe that the Palin companion animals aren't ordinarily pampered, and we wish the entire family a peaceful and humane 2015," Newkirk said.