The attacker tried to enter the Dargah Fatehpur in the Jhal Magsi district of Balochistan and blew himself up when he was stopped by the police at the main entrance, Deputy Commissioner Asadullah Kakar told the media.
Kakar confirmed the death toll and said one police constable was killed while attempting to stop the suicide bomber from entering the shrine.
Two other policemen were also injured in the blast.
Devotees gather at the shrine of the revered Sufi saint every Thursday to participate in a dhamaal and prayers.
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Balochistan Home Minister Mir Sarfaraz Bugti told the media that so far it appeared to be a suicide attack.
"Investigations are still continuing and the injured have been moved to the district headquarters hospital in Jhal Magsi," Bugti said.
Balochistan government spokesman Anwarul Haq Kakar confirmed that it was a suicide attack.
No group claimed responsibility for the attack but the Taliban usually target shrines as they consider it un-Islamic.
The local administration declared an emergency at hospitals in Sibbi and Dera Murad Jamali.
Today's is the second major attack at a shrine in Balochistan where in November 2016, at least 52 people were killed and 102 injured in a blast at the shrine of Shah Norani in Khuzdar district.