A spokesman for medical charity Edhi said the attacker appeared to have targeted the women's wing of the shrine, and around 30 children accompanying their mothers were dead.
Islamic State, the Middle East-based militant group which has a small but increasingly prominent presence in country, claimed responsibility for the attack, the group's affiliated news agency AMAQ reported.
Senior police officer Shabbir Sethar told Reuters from a local hospital that the death toll was likely to rise.
"At least 76 are dead and over 150 have been injured," Sethar said by telephone.
Television footage from the famous Lal Shahbaz Qalandar shrine in the town of Sehwan Sharif showed army and paramilitary medical teams reaching the site and injured people being taken to nearby hospitals in ambulances and a military helicopter.
"We were there for the love of our saint, for the worship of Allah," a wailing woman told the private television channel outside the shrine, her headscarf streaked in blood. "Who would hurt us when we were there for devotion?"
In August last year, at least 74 people, mostly lawyers, were killed in a suicide bombing of a hospital in Quetta.
SINDH SUFIS
"Each drop of nation's blood shall be revenged, and revenged immediately. No more restraint for anyone," Army Chief Qamar Bajwa said in a statement.
Shortly after the blast, the army announced it was closing the border with Afghanistan with immediate effect for security reasons. Insurgents operate on either side of the neighbours' long and porous frontier.
Different militant groups, often trying to outdo each other, say they are responsible for the bombings.
In the case of the Quetta hospital blast, both a faction of the Pakistani Taliban - Jamaat-ur-Ahrar - and Islamic State claimed responsibility.
Jamaat also said it was responsible for a bombing in the eastern city of Lahore earlier this week that killed 13 people.
Prime Minister Nawaz Sharif quickly condemned the bombing, decrying the assault on the Sufi religious minority.
He vowed to fight Islamist militants, who target the government, judiciary and anyone who does not adhere to their strict interpretation of Sunni Islam.
"The past few days have been hard, and my heart is with the victims," Sharif said. "But we can't let these events divide us, or scare us.