No group immediately claimed responsibility for the attack.
"The courageous police constable stopped the suicide bomber from entering the shrine after which he blew himself up".
Kakar added later that 13 people had been killed, and 20 others were seriously injured.
According to city police chief Mohammad Iqbal, the critically injured were being shifted to relatively better equipped hospitals in nearby districts.
A representative of the Balochistan Government stated that the explosion was a suicide attack, adding that the Police tried to stop the attacker but he blew himself up.
The shrine is in Jhal Magsi, near the provincial capital Quetta.
Provincial Home Minister of Balochistan Sarfraz Bugti said the blast happened during the Urs (death anniversary of the shrine's saint) celebrations at the Fateh Pur shrine.
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Balochistan government spokesman Anwarul Haq Kakar too confirmed that it was a suicide attack.
The bomber blew up his explosives at a time when the shrine was packed.
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.
The local administration also declared an emergency at hospitals in Sibbi and Dera Murad Jamali.
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.
IS and other Sunni extremists perceive Shiites as apostates who should be killed and have carried out many such attacks in the past, targeting minority Shiite Muslims in Baluchistan and elsewhere in the country.
Prime Minister Shahid Khaqan Abbasi has condemned the attack on the shrine.