The attack took place at Dargah Fatehpur in the Jhal Magsi district of the oil and gas rich Balochistan province, bordering Iran and Afghanistan.
Later, addressing reporters, Balochistan home minister Mir Sarfaraz Bugti said that so far it appeared to be a suicide attack.
He added that one police constable was killed while attempting to stop the suicide bomber from entering the shrine, while two other policemen were injured in the blast.
"The custodian of the shrine Syed Sarfraz Shah was present in the shrine when the suicide bomber tried to enter the place but blew himself up outside as policemen stopped him, at least 15 people are confirmed dead", Naseerabad commissioner told media.
Police said there were around 800 to 1,000 people inside the shrine when the incident happened.
The shrine is in Jhal Magsi, near the provincial capital Quetta.
The bomber blew up his explosives at a time when the shrine was packed.More news: NYC Subway Ads Calling The Knicks "Hopeless" To Be Removed
The local administration declared an emergency at hospitals in Sibbi and Dera Murad Jamali.
There was no immediate claim of responsibility but militants and separatists have repeatedly targeted minority Shia Muslims at religious sites, as well as security officials.
Initial probe showed that the blast occurred when dhamal was going in the premises of the shrine.
The government authorities have confirmed the death of at least 18 people in the blast.
Shrines across Pakistan have been attacked in past by extremists who consider it un-Islamic to praying at the tombs of saints.
Pakistani Prime Minister Shahid Khaqan Abbasi condemned the attack, saying that "terrorists have no religion" and that his government will act against militants with full might.