Praising the Sindh Police, Chaudhry Nisar Ali Khan announced here that the arrests were the result of an "excellent coordination between police and intelligence agencies."
The minister did not disclose when the arrests were made or provide any details on the affiliation of the attackers.
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Prime Minister Nawaz Sharif's office has also confirmed the arrests in a statement.
"Prime Minister Nawaz Sharif talked to CM Sindh on phone and appreciated the law enforcement agencies, especially police, on arresting four persons responsible for Safoora Chaurangi incident," it said.
Both a Pakistani militant group linked to Islamic State and a Taliban splinter group have claimed responsibility for the May 13 assault.
It was the first official claim of responsibility by the IS leadership of an attack in the Afghanistan-Pakistan region.
Kalashnikov-wielding militants donning police uniforms had shot 45 Shia Ismaili Muslims in the head as they attacked their bus in Karachi city.
The bus was carrying over 60 people from the group when the militants barged into it near Safoora Chaurangi.
The attackers killed 45 people - 26 men and 17 women - and wounded over 20 others before fleeing from the scene.
The passenger bus, run by a welfare service of the Ismaili community, was attacked by six unidentified men on three motorcycles.
Sharif said the arrest of plotters of this heinous crime in such a short time proves that Karachi operation is going in the right direction and that law enforcement agencies have the capability of handling such challenging tasks.
Karachi with population of over 18 million is facing violence by militants and criminals and government had launched an operation to create peace.
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