According to city police chief Mohammad Iqbal, the critically injured were being shifted to relatively better equipped hospitals in nearby districts.
Provincial government spokesman Anwarul Haq Kakar told ARY News that the police had tried to confront the suicide bomber, which resulted in the death of a policeman.
A ceremony of Urs was going on in the shrine when the incident happened, he added.
Pakistani devotees gather around the bodies of blast victims after a suicide bombing near a sufi shrine in the Gandawa area of Jhal Magsi district on October 5, 2017.
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Jhal Magsi is located at a three-hour drive from Jacobabad and Larkana.
Sarfraz Bugto, the provincial home minister, said "terrorists have shown their inhumaneness by attacking innocent civilians".
DPO Jhal Magsi said a constable was killed while attempting to stop the suicide bomber from entering the shrine.
There was no immediate claim of responsibility but militants and separatists have repeatedly targetted minority Shiite Muslims at religious sites, as well as security officials.
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"We have confirmed reports it was a suicide attack", he said.
The local administration has declared an emergency at hospitals in Sibbi and Dera Murad Jamali.
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.
The attack, which came as the latest sectarian attack in troubled Baluchistan province, is also the second major attack at a shrine in Balochistan in a year.
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Todays attack is the second major strike 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.