The suspected bomber was an engineering student born in 1987 who had recently begun to take an interest in the ideas of hardline Islamists, the ministry said in a statement on Monday.
It named him as Hasan Rafat Ahmad Bashandi, who lived in the north Cairo suburb of Shubra al-Khaima and went to the Benha branch of Zagazig University in the east of the Nile delta.
Egyptian prosecution sources had earlier named him as Muhammad Subhi Ali Jidan.
"All the evidence indicates that while the perpetrator was preparing the bomb for explosion, the explosion took place," the statement said.
Egyptian police added that they have detained 30 people, including the bomber's mother, three brothers and 16 other relatives.
The bomber's badly damaged body was found in the street in the Muski area of old Cairo, where the device exploded.
The explosion on Thursday killed a French woman, a French man and an American man, as well as the bomber. Eighteen people were wounded - 11 Egyptians and seven foreigners.
Egyptian officials have repeatedly said the bomber did not appear to have been part of an organised group.
The explosion targeted foreign
tourists at a popular Cairo spot
The ministry statement said Bashandi was carrying a leather bag containing about 3kg of explosives and a large quantity of nails.
At his aunt's house, police found 42 containers of fireworks from which the gunpowder had been emptied, it added.
The police have detained two of the suspect's brothers and his mother in order to test their DNA to match it with.
"After his father died in August last year, he started to be excessively committed to certain religiously extremist ideas and tried to force his family not to watch television," the Egyptian Interior Ministry statement said.
"He showed signs of emotion and tension about the course of events internationally and regionally - a source of dispute between him and his mother."
In a search of his house, police found compact discs on which he had stored writings by hardliners on jihad, combat operations and on how to make primitive bombs from materials available in the market, all downloaded from the internet.
The family's neighbours said they were shocked and surprised that Bashandi had been identified as the bomber.
Sayid Shabl, the owner of a restaurant near their house in the industrial part of Shubra al-Khaima, a mainly working-class area, said: "They are good people and what you hear from me, you will hear from a hundred others. They were very quiet and polite. Their mother is a wonderful woman."