The envoy, Kyriakos Amiridis, had been missing since Monday.
His body was found in the boot of a burnt-out car on the outskirts of Rio de Janeiro on Thursday.
Police suspect Mr Amiridis, 59, was the victim of a "crime of passion". His Brazilian wife, Francoise Amiridis, and a local policeman are being questioned.
Police in Rio are working on the assumption that Mrs Amiridis was having an extramarital affair with the detained policeman and had conspired to kill him, local media reported.
The couple had been living together for 15 years and their daughter is 10 years old, local news programme RJTV reported.
Two other men have been held for questioning. Police initially said they were both implicated in the murder, but they later stated that one of the men was only a witness.
Mr Amiridis served as consul in Rio de Janeiro between 2001 and 2004 and returned to the country as ambassador earlier this year.
He had travelled from Brasilia to the city of Nova Iguacu, north of Rio, to spend the Christmas holidays there with his wife and her parents.
Mrs Amiridis reported her husband missing on Wednesday.
She told police that he had left the flat in the car he had rented on Monday evening without telling her where he was going.
The burnt-out car was found on Thursday under a flyover on one of the main access roads to Rio with a body inside.
The body was burned beyond recognition, but Rio police said it was that of Mr Amiridis.
Investigators also said that they had found blood stains on the sofa in the flat the couple was staying in.
They told local media that they thought Mr Amiridis had been killed in the flat before his body was taken away in his rental car.
Police in Rio de Janeiro have detained the Greek ambassador's wife and two other people on suspicion of involvement in his murder.