New York-based Human Rights Watch said it submitted the request to Argentina's federal judge Ariel Lijo on Monday.
HRW's Middle East and North Africa director Sarah Leah Whitson said the international rights group took the case to Argentina because Prince Mohammed, also known as MBS, will attend the opening of the G20 summit this week in Buenos Aires.
Argentina's constitution recognises universal jurisdiction for war crimes and torture, meaning judicial authorities can investigate and prosecute those crimes no matter where they were committed.
"We submitted this info to Argentine prosecutors with the hopes they will investigate MBS's complicity and responsibility for possible war crimes in Yemen, as well as the torture of civilians, including Jamal Khashoggi," said Whitson.
"There's an extremely strong basis for Argentina to closely examine a very broad record of documentation and facts. People around the world are desperate to see real accountability for people who are getting away with terrible crimes," she told Al Jazeera.
Argentine media cited judicial sources as saying it was extremely unlikely authorities would take up the case against the crown prince, Saudi Arabia's de facto ruler.
The killing of Khashoggi, a Washington Post columnist and a critic of the crown prince, at Riyadh's consulate in Istanbul on October 2 has strained Saudi Arabia's ties with the West and battered Prince Mohammed's image abroad.