Deputy Commissioner Anwar-ul-Haq Kakar told that the explosion took place at the gate of the shrine.
In February, a suicide bomber had killed more than 80 people and injured 250 others in an attack on the shrine of Lal Shahbaz Qalandar in Sehwan Sharif in Sindh.
At least two policemen were also injured in the blast.
Islamic State claimed responsibility for the attack via its Amaq news service.
Meanwhile, Balochistan Home Minister said that he has instructed concerned authorities to respond immediately.
According to ARY News correspondent Moosa Baloch, a suicide attacker blew himself up outside the Dargah leaving a policeman dead and injuring a huge number of devotees at a time when the custodian of the shrine was holding a special meeting. "If he had managed to enter the shrine there would be have been greater casualties", Bugti said.
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The shrine is located four kilometres away from the city and the nearest hospital in the area can only accommodate 12 people, so the rescue teams are shifting the injured people to hospital in neighbouring districts. The village is about 400km east of Quetta, the capital of Baluchistan province.
A bomb attack on the same shrine killed 35 people in 2005.
In November 2016, at least 52 people were killed when a suicide blast had roacked the Shah Noorani shrine near Hub in Balochistan's Lasbella district.
The police have launched an investigation and an initial probe reportedly showed that the blast occurred when dhamal was ongoing in the premises of the shrine.
Incidents involving attacks on religious places are not unique in Pakistan as the militant groups often carry out such attacks, specifically when a ritual is process in such sites.
Earlier, unconfirmed reports indicated that the death toll has further increased to fourteen people but the local officials have not confirmed the toll so far.