The Swedish Chancellor of Justice, Göran Lambertz, was asked to probe whether the report in the Aftonbladet tabloid last month amounted to inciting racial hatred and violated freedom of expression laws.
The TT news agency said the Chancellor of Justice had decided not to open a preliminary investigation into the case.
The Chancellor of Justice, who was unavailable for comment on Saturday, is a government-appointed official who acts as an independent judicial watchdog and is the only prosecutor in Sweden who can take legal action in cases concerning freedom of speech.
Aftonbladet alleged in a story in August that Israeli soldiers had been involved in the illegal harvesting and trafficking of human organs.
The claims sparked outrage in Israel and prompted senior figures in the Israeli government to demand that Sweden condemn the report.
But Swedish Prime Minister Fredrik Reinfeldt rebuffed the calls, stressing a free press is an integral part of democracy.