"Foreign Minister Hector Timerman has given the order not to accept the slightest move to allow the return of the body of Nazi criminal Erich Priebke to our country," the foreign ministry said in a tweet.
"Argentines will not accept this kind of affront to human dignity."
Priebke died Friday in Rome aged 100 after serving nearly 15 years under house arrest for a World War II massacre in Italy.
His lawyer Paolo Giachini had said he would be buried near his wife in Argentina, where he fled after the war.
Priebke lived for more than 40 years in the city of Bariloche, in southwest Argentina, where he was arrested in 1994 and then extradited to Italy for trial.
He was sentenced to life in prison in 1998 for his role in a bloodbath at Rome's Ardeatine caves in March 1944 that left 335 people dead, including 75 Jews.
But because of his age and ill-health he was allowed to serve out his life sentence at Giachini's home.
Nicknamed the "butcher of the Ardeatine caves", Priebke always insisted that he had only ever obeyed orders.
Two Jewish organizations, the Israelite Argentine Mutual Aid Association (AMIA) and the Delegation of Argentine Jewish Associations (DAIA), welcomed the refusal by Buenos Aires.
The fact that Priebke had "resided with impunity for decades in our country, enjoying a life that so many civilians had been deprived of" was "an affront to the principles of the Republic," the DAIA said.
It urged people "not to forget and not forgive the Nazi genocide, or any type of genocide."
Argentina's Jewish community is the largest in Latin America, consisting of some 300,000 members.