The police now have nine people in custody in connection with the attack, which killed three tourists and the bomber.
The police have named the bomber as Hasan Rafaat Ahmad Bashandi, an engineering student born in 1987 who had recently begun to take an interest in hardline Islamist ideas.
"Today police forces detained three people ... connected to the accused in the Cairo bombing incident," a police official said on Thursday.
The official said the three latest people to be detained lived in Minya governorate, about 200km south of Cairo, but gave no more details about them.
The official said police forces were searching for an unidentified person in Shubra al-Khaima, north of Cairo, who they believed instructed Bashandi the day before to carry out the attack.
The six other people detained by police lived in the same district, including his aunt, mother and two of his brothers.
Police found 42 firework containers, emptied of gunpowder, at Bashandi's aunt's house.
"Today police forces detained three people ... connected to the accused in the Cairo bombing incident"
Cairo police official
The bomb killed a French woman, a French man, an American man and Bashandi. It also wounded 18 people - 11 Egyptians and seven foreigners.
It was the worst attack on foreigners in Egypt since 1997, when Islamists killed 58 tourists and four Egyptians at a Pharaonic temple near the southern town of Luxor.
Egyptian officials say the bomber does not appear to have been part of an organised group.
Two bombers were killed at the Hilton hotel in the Red Sea resort of Taba last October.
The authorities said their bomb exploded before they had time to get away. The organiser was a Palestinian and the target appeared to be Israeli tourists.