Local officials said the blast took place after a bomber detonated his explosives outside the site in Jhal Magsi district, which is located about 400 kilometers east of Quetta, the capital of Balochistan province.
Mohammad Iqbal, a district police chief, said five children, a woman and one police officer were among those killed in the bombing.
Anwarul Haq Kakar, spokesman for the provincial government, said the death toll could rise as some of the wounded were in a critical condition.
The bomber blew up his explosives at a time when the shrine was packed.
Local TV footage showed people crying for help in the immediate aftermath of the attack.
No group immediately claimed responsibility for the attack.
Sarfraz Bugto, the provincial home minister, said "terrorists have shown their inhumaneness by attacking innocent civilians."
Pakistani Prime Minister Shahid Khaqan Abbasi condemned the attack. In a statement, he said that "terrorists have no religion" and that his government would act against militants with full might.
A bomb attack on the same shrine killed 35 people in 2005.
In November last year, at least 52 people were killed in a bombing at a shrine in the Hub district south of Jhal Magsi.
In mid-February, a bombing by the Daesh Takfiri terrorist group on a shrine in the city of Sehwan in Sindh province killed at least 80 people, including 20 children, and injured some 250 others.
Pakistan has been witnessing violent terrorist attacks over the past decade. Militants with the Pakistani Taliban have largely been blamed for the violence, but responsibility for some of the bombings was claimed by Daesh terrorists.
Pakistan estimates that there have been 70,000 casualties in militant attacks since it joined the US campaign against militants after the September 11, 2001 attacks.