The cartoon, by Gerald Scarfe, showed Netanyahu building a wall with the blood and limbs of Palestinians and was published on January 27 - International Holocaust Remembrance Day.
The caption on the image read: "Israeli elections - will cementing peace continue?"
Jewish groups condemned the move, with the Board of Deputies of British Jews complaining to the Press Complaints Commission.
Middle East Special Envoy Tony Blair expressed his "sharp reservations" about the piece, while the European Jewish Congress President Moshe Kantor called it "sickening" and demanded an apology.
Murdoch, News Corp Chairman and CEO, tweeted: "Gerald Scarfe has never reflected the opinions of the Sunday Times. Nevertheless, we owe major apology for grotesque, offensive cartoon."
A Sunday Times statement said: "This is a typically robust cartoon by Gerald Scarfe. It is aimed squarely at Mr Netanyahu and his policies, not at Israel, let alone at Jewish people.
"It appeared yesterday because Mr Netanyahu won the Israeli election last week."