The UN human rights office on Tuesday said the investigation should encompass all aspects of his treatment during nearly six years of his incarceration.
Egypt's first democratically president was buried in a small family ceremony early on Tuesday a day after he suffered a fatal heart attack in a Cairo court, his sons said.
"Concerns have been raised regarding the conditions of Mr Morsi's detention, including access to adequate medical care, as well as sufficient access to his lawyers and family ...," UN human rights spokesman Rupert Colville said in a statement.
"The investigation should be carried out by a judicial or other competent authority that is independent of the detaining authority and mandated to conduct prompt, impartial and effective investigations into the circumstances and causes of his death," he said.
Morsi was overthrown on July 3, 2013, after barely in power for a year in a coup staged by current President Abdel Fattah el-Sisi and placed under house arrest before being moved to prison.
ya to pay their respects.