The ministry said investigations revealed the group was led by a suspect who received financial and logistical support and instructions to carry out the attacks by Brotherhood leaders residing in Qatar.
The Muslim Brotherhood have denied any involvement with the explosion at the Saint Peter and Saint Paul Church on Sunday.
The incident was the deadliest attack in recent memory on the Christian minority, who make up about 10 percent of Egypt's population.
In a statement, the interior ministry said investigations showed 22-year-old Mahmoud Shafiq Mohammed Mustafa, the suspected suicide bomber, had been arrested in 2014 while securing Muslim Brotherhood convoys while armed. He was released in May the same year.
DNA testing of body parts found at the scene matched with his family, according to the interior ministry.
The suspect's lawyer said Monday that Mustafa had been arrested and beaten by police two years ago after allegedly taking part in an Islamist demonstration.
If independently confirmed, Mustafa would be the latest Egyptian to be radicalised after being subjected to police abuse, a practice that was common for decades and has become rampant after a crackdown on dissent following the military's 2013 ouster of an Islamist president.
Mahmoud Hassan, one of Mustafa's lawyers, said his client, who was 16 at the time of his arrest, was tortured until he confessed to the possession of weapons and explosions. He also faced charges of membership in an "illegal organisation," Egyptian parlance for the outlawed Muslim Brotherhood, the Islamist group of which former President Mohammed Morsi was a senior official.
Inflaming sectarian strife
The Interior Ministry said late Monday that Mustafa belonged to a terrorist cell founded by an Egyptian doctor and funded by Muslim Brotherhood leaders living in exile in Qatar, long accused by Egypt of supporting militants groups. It said the cell was tasked with staging attacks that would lead to sectarian Muslim-Christian strife.
After his arrest, Mustafa spent nearly two months in detention before being released on bail. A court later convicted him in absentia, according to the lawyer. Traumatised by the torture, he told his lawyer not to appeal, fearing he would be abused again if detained.
A police photo of Mustafa and a friend arrested on the same day showed the pair, clearly in their teens, with bleeding noses and bruised faces. Placed atop a coffee table in front of them was a rifle, ammunition and what appeared to be a homemade bomb.
Hassan insisted that Mustafa was not a member of the Brotherhood, but the young Egyptian student from the oasis province of Fayoum appears to have been radicalised by his experience in detention, a danger many Egyptian rights activists warn the government against.
No one has so far claimed responsibility for Sunday's bombing. Two active militant groups believed to have links to the Muslim Brotherhood - Hasm and Liwa el-Thawra - distanced themselves from the attack. The local affiliate of the Islamic State group has so far remained silent.
Sunday's bombing was among the deadliest attacks in recent memory to target Egypt's Coptic minority, which makes up around 10 percent of the country's population and strongly supported the Sisi-led military overthrow of Morsi, Egypt's first freely elected president whose one year in office proved to be divisive.
Since then, Islamic militants have carried out scores of attacks, mainly targeting the security forces, while the government has waged a wide-scale crackdown on dissent.
