Kathy Griffin apologized for the picture -- released on Tuesday by the celebrity photographer Tyler Shields -- after a tirade of criticism from conservatives and liberals, saying in a video "I beg for your forgiveness" for having "crossed a line."
"Kathy Griffin should be ashamed of herself," Trump tweeted. "My children, especially my 11 year old son, Barron, are having a hard time with this. Sick!"
Griffin, an outspoken Trump critic who won two Emmy awards for her reality show "My Life on the D List," said she would ask Shields to remove the image from the internet.
"I sincerely apologize. I'm just now seeing the reaction of these images. I'm a comic. I crossed the line," she said in a video posted to social media late Tuesday.
"I beg for your forgiveness. I went too far. I made a mistake and I was wrong," she added in the 31-second clip.
Among those who slammed the photograph was Trump's son Donald Trump, Jr. "Disgusting but not surprising," he tweeted. "This is the left today. They consider this acceptable."
"Our politics have become too base, too low & too vulgar, but Kathy Griffin's post descends into an even more repugnant & vile territory," wrote defeated 2012 Republican presidential nominee Mitt Romney.
"It is never funny to joke about killing a president," she tweeted.
CNN anchor Anderson Cooper, who co-hosts a New Year's Eve program with Griffin on the network, tweeted that he was "appalled" by the photo shoot.
"It is clearly disgusting and completely inappropriate," he added.
CNN called the picture "disgusting and offensive" in a statement, adding that it was "evaluating our New Year's coverage."
The Secret Service said it would look into the incident, posting on Twitter that "threats made against @SecretService protectees receive the highest priority of all of our investigations."
Squatty Potty, a Utah-based bathroom products company, suspended an advertising campaign featuring Griffin, calling the picture "deeply inappropriate" and "contrary to the core values our company stands for."