The guided tour comes ahead of a mission to Geneva by Egyptian officials for a review on Wednesday before the United Nations Human Rights Council.
It was arranged in response to a stinging review last week by an independent panel of UN experts that blasted conditions in Tora.
The experts said the death of ousted Islamist president Morsi, who was held in Tora for five years, could amount to a "state-sanctioned arbitrary killing".
The former president died in June after collapsing in a Cairo courtroom while on trial.
"Morsi was held in conditions that can only be described as brutal, particularly during his five-year detention in the Tora prison complex," the experts said in a statement.
His death "after enduring those conditions could amount to a state-sanctioned arbitrary killing", the experts added. They also warned that thousands are at risk of death in the same prison.