Attorney General Mahir Abd al-Wahid said on Saturday that Ashraf Said Yusuf died in hospital on Thursday from injuries that were self-inflicted.
Police informed prosecutors on 11 May that their prisoner had become "very agitated and deliberately hit his head on the wall of his cell", prompting his transfer to hospital.
Earlier injuries sustained while on the run from police might have contributed to his death, the attorney general said, adding that a full report on the circumstances is being prepared.
Yusuf sustained injuries to his hand and leg on 22 April when he jumped off the entrance to a highway tunnel in Cairo in an attempt to evade arrest, the attorney general said.
Key tourism sector
A policeman spotted the suspect in the Cairo neighbourhood of al-Duqqi, recognised his face and pursued him.
The policeman "tried to arrest him but he managed to escape, jumping off the al-qalaa tunnel in front of the Sheraton Hotel in Cairo and under a passing truck," Abd al-Wahid said.
Yusuf also threw himself out of the window of an apartment in Menuf, north of Cairo, on 29 April after realising that police were closing in on him.
But locals "managed to catch him and they assaulted him in order to prevent him from escaping after finding out that he was one of the terrorist elements being sought by security organs", the attorney general said.
Yusuf was suspected of masterminding a deadly 7 April bombing of a Cairo bazaar that was followed by two further attacks on 30 April targeting Egypt's tourism industry - a key foreign exchange earner.