"There is no justification for the State of Gaza being able to shoot at our towns with impunity," he wrote. "We need to flatten entire neighborhoods in Gaza. Flatten all of Gaza. The Americans didn't stop with Hiroshima - the Japanese weren't surrendering fast enough, so they hit Nagasaki, too.
"There should be no electricity in Gaza, no gasoline or moving vehicles, nothing. Then they'd really call for a ceasefire.
"Were this to happen, the images from Gaza might be unpleasant - but victory would be swift, and the lives of our soldiers and civilians spared."
Sharon said the alternative is a complete re-occupation of the Gaza Strip.
The opinion piece has prompted an angry reaction on social media, with many on Twitter saying Sharon is advocating genocide, while commenters on the story also blasted the Jerusalem Post for publishing the article.
"Gilad Sharon writes an OpEd effectively suggesting genocide as the answer to the conflict, and it gets published in the JPost. This is disgusting," Ron wrote.
"Disgusting article. Ok for IDF to kill civilians including children because some of their relatives may have voted for Hamas? Why is this published?" Jem said.
Sharon's father Ariel served as Prime Minister of Israel from 2001 to 2006. While for decades Sharon supported Israeli settlements in the West Bank and Gaza Strip, in the mid-2000s he was behind the withdrawal of thousands of settlers as part of the internationally endorsed Road Map. He has remained in a coma following a stroke in 2006.