The "Like A Virgin" hitmaker was confirmed as the Tel Aviv event's headliner last week (end April 14), sparking an outcry from activists angered by the Israeli government's treatment of Palestinians living in the occupied territories.
Roger is a prominent supporter of the Boycott, Divestment and Sanctions (BDS) movement demanding artists and firms cut cultural and economic ties with Israel.
He has previously called for Eurovision to be moved, and has now penned an article in The Guardian newspaper asking Madonna not to perform.
"In the context of the current conversation about the location of the Eurovision finals and the participation of Madonna and the other performers, the brothers and sisters in question are the people of Palestine who live under a deeply repressive apartheid regime of occupation and do not enjoy the right to life, liberty and self-determination," he wrote in his piece.
The former Pink Floyd rocker went on to urge Madonna and the contestants from 41 countries to pull out and read the United Nations Universal Declaration of Human Rights to better understand his objections.
The pop superstar, who has yet to respond to Roger and other dismayed fans, will reportedly be paid $1 million (£770,000) by an Israeli businessman for a two-song performance in Tel Aviv.
In recent years Roger has badgered numerous artists to reconsider their Israel tour dates, although his words have provoked an angry backlash from some acts, including Radiohead and Nick Cave, who have refused to cancel concerts.
The Eurovision Song Contest final, which was won last year by Israeli singer Netta Barzilai, takes place on May 18.