There are claims that organs were taken from bodies without proper efforts to find the relatives and obtain their consent, prosecutors told the BBC.
The Coroner's Service in Sao Paulo is the focus of the investigation.
Officials of the Coroner's Service, or SVO, deny any illegal activity, saying procedures were followed at all times.
Until recently, people who died in the street or in public hospitals were buried as paupers if their bodies were not reclaimed by relatives within 72 hours. The SVO says procedures have since been improved.
Selling organs is against Brazilian law.'Mass graves'
Sao Paulo's office of public prosecutors told the BBC their investigation, which began last November, was prompted by claims from relatives who said authorities had not made proper efforts to contact them before their loved ones were buried in the cemetery of Perus.
Later, two witnesses also told prosecutors that organs from some of the bodies had been removed and sold for medical research.
Prosecutors say they currently have no material proof of trade in human organs.
But investigations suggest that over the last 15 years the bodies of 3,000 people have been taken from the autopsy centre to mass graves - even though they had documents identifying them.'No legal obligation'
The SVO is run by pathology teachers from the Faculty of Medicine of the University of Sao Paulo - one of Brazil's most prestigious universities.
The SVO's director, doctor Luiz Fernando Ferraz da Silva, told BBC Brasil that the service acts "strictly within the law" and that bodies are "generally... buried intact".
"There are specific situations in which organs are used, but always with the purpose of being used for research," he said.
"But where patients' bodies are not claimed, that does not happen."
When asked about the allegations that organs were sold for medical research, he said that information required by the investigating authorities would be sent directly to them.
The service had no legal obligation to search for family members of dead people taken to its premises, he added.Maria Cecilia Leao Correa's story
Maria Cecilia Leao Correa's father was buried in the Perus Cemetery as a pauper, after he went missing and spent nine days in a public hospital.
After making a police report, Ms Correa learned of his fate through the Coroner's Service. "They told me that his body remained there for 72 hours, but since nobody went there to reclaim it, he ended up being buried in a mass grave," she said.
Ms Correa says that her "father had his ID on him but the Coroner's Service did not make any effort" to contact her.
"There was even a police report on his death," she said.
"All that was needed was a mouse click. How was I to guess that he was at this Coroner's Service?"
After learning where he was buried, she tried to transfer his body to the family tomb.
"But the gravedigger said it wasn't worth it," she said, adding that he told her that her father had been buried with no organs, and was totally unrecognisable.
When questioned by BBC Brasil about the circumstances of her father's death, Dr Ferraz da Silva said he did not evaluate "each case individually" and would not be able to "check and verify the specific case" of Ms Correa's father.
"There are situations of dead people who had six telephone numbers to be contacted, but whose families were not contacted," she said.
Families often struggled to identify the whereabouts of deceased family members, Ms Vendramini added.
"Few people know what the Coroner's Service does; that is why the bodies are not reclaimed within the right period."
The SVO said they had improved their identification procedures following a critical newspaper report last month.
"The Coroner's Service is now collecting information with pictures of the face of the deceased, identification marks, fingerprints and tissue fragments," Dr Ferraz da Silva said.
"That information is then sent to the police missing persons department. Bodies are only buried ten days after that information is reported."
He also said that the number of mistaken burials had diminished over the past decade, from an average of 400 cases per year to about 100 cases per year.