His body was found Thursday in the trunk of the charred vehicle he had rented earlier.
Mr Amiridis had been on holiday with his family in Rio de Janeiro's northern Nova Iguacu area since 21 December.
The ambassador's wife, Francoise Amiridis, has now arrived at a police station in the Rio area for questioning.
Amiridis, 59, had been missing since Monday.
In Athens, Greek foreign ministry spokesman Stratos Efthymiou said the government had no comment about the case.
It reported that police "suspected" the body inside to be that of the ambassador.
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The burnt-out auto was found on Thursday under a flyover on one of the main access roads to Rio with a body inside.
The auto was located in the northern outskirts of Rio, a poor section dominated by powerful and politically connected armed groups mostly comprised of off-duty or retired police and firefighters who control vast areas.
He was reported missing by his wife on Wednesday, according to a state police official cited by Reuters.
Rio police inspector Evaristo Pontes had earlier told Brazilian media that he did not believe the ambassador was kidnapped. He had previously served as Greece's consul general in Rio from 2001 to 2004.
"The ministry and the Greek embassy in Brasilia are monitoring closely the case and shall, in close cooperation with the Brazilian authorities, proceed with all the necessary actions", it added.
Rio suffers from a high crime rate, and violent crime is not uncommon.