In the cartoon, Mr. Bezos, Meta founder Mark Zuckerberg and OpenAI’s Sam Altman are depicted on their knees handing bags of cash to a statue of Trump.
Mickey Mouse in the cartoon is also depicted prostrate. Disney-owned ABC News last month agreed to pay $15 million to settle a defamation lawsuit filed by Trump.
Ms Thelness announced her resignation in a post to Substack on Friday, saying she had been with the paper since 2008.
“In all this time, I have never killed a cartoon because of who or what I chose to aim my pen at,” she wrote. “Until now.
“The Cartoon That Was Killed Criticizes Billionaire Tech and Media CEOs Who Have Been Doing Everything to Ingratiate themselves with President-Elect Trump.”
She said the cartoon satirizes “these people with lucrative government contracts and an interest in deregulation.”
But Mr Shipley told the BBC that he had decided not to publish the cartoon because of the repetition of another piece which was due to be published.
“I respect Anne Thelnes and all she has given The Post. But I have to disagree with her interpretation of events,” he said in a statement. “Not every editorial opinion is a reflection of a pernicious force.”
He added: “I was guided by the fact that we had just published a column on the same topic as the cartoon and had already planned to publish another column – this time on satire.”
This is not the first time that one of Ms. Telnes’ cartoons has made it to the Washington Post.
In 2015, the newspaper retracted one of her sketches in which the young daughters of Texas Senator Ted Cruz were depicted as monkeys.
Explaining its decision at the time, the paper said it was its editorial policy not to allow children.
Last month, Mr. Bezos announced that Amazon would donate $1 million to Trump’s inaugural fund and make $1 million in kind.
Mr Bezos also described Mr Trump’s re-election victory as an “extraordinary political comeback” and dined with him at the president-elect’s Mar-a-Lago residence in Florida.
The paper faced a liberal backlash in the weeks before November’s presidential election after Mr. Bezos intervened to prevent the editorial board from endorsing Vice President Kamala Harris.
Mr Bezos defended the move, but the paper said he had lost more than 250,000 followers since the decision.
The Los Angeles Times, whose owner Patrick Soon-Shiong is also pictured in the now-killed cartoon, took a similar step and said the paper would not publish its endorsement of Harris in October.
