Sindh Health Secretary Fazal Pecheho also said the number of people injured in Thursday's attack had climbed to 200.
A local hospital official, Dr. Zahid Hussain, earlier told CNN that 24 of the dead were children aged four to eight. Another 16 of the victims were women, he said.
Thousands of worshipers, including families with their children, had gathered Thursday at the more than 800-year-old shrine for the Sufi ritual of Dhamal, which involves music, chanting and prayer.
The Islamic State Khorasan, ISIS' affiliate in Afghanistan and Pakistan, claimed responsibility for the attack in a phone call to CNN.
Prime Minister: 'Brutal' attack
In the aftermath of the blast, all the dead and injured were taken to the nearby 100-bed Sehwan Hospital, which was overwhelmed by the sudden influx of patients, Hussain told CNN.
Many have since been transferred to bigger hospitals in other cities of Sindh province, he said.
The Amaq news agency, which is affiliated with ISIS, reported the attack was carried out by a suicide bomber in an explosives vest.
Pakistani Prime Minister Nawaz Sharif called the attack "brutal."
"I have directed all the state institutions to mobilize all resources for rescue and relief after this brutal terror attack on Lal Shahbaz Qalandar's shrine," Sharif said in a statement.
The Pakistani military said Friday that the capital, Islamabad, and its twin city of Rawalpindi had been put on high alert following "a recent upsurge in terrorist incidents in the country." As a result, schools in Islamabad and Rawalpindi closed early.
Search operations in the Rawalpindi area have been stepped up, according to the statement from the ISPR, the media wing of the Pakistan Armed Forces. Senior law enforcement agency officials also met Friday to assess the security situation and ways to respond to the terror threat.
"Security forces and intelligence outfits have been instructed to further intensify combing and targeted operations with the aim to eliminate terrorists and sleeper cells," the statement said.
n a series of tweets, Pakistani military spokesman Maj. Gen. Asif Ghafoor blamed operatives from Afghanistan for a recent spate of attacks on the country and urged the country to remain calm.
He later announced that the Pakistan-Afghanistan border was "closed with immediate effects till further orders due to security reasons."
The office of the Afghan President, Ashraf Ghani, said on Twitter that he "condemns (the) terrorist attack in Pakistan and terms ISIS a common enemy of Afghanistan & Pakistan."
Sediq Sediqqi, spokesman for the Afghan Ministry of Interior Affairs, tweeted that the Islamic State Khorasan poses an "enormous threat" to both the Afghan and Pakistani people and called for the two countries to work together to "eliminate" the extremist group.
The Sehwan attack comes days after a bomb exploded during a protest in Lahore, Pakistan, on Monday, killing at least 14 people and injuring 59 more, according to government spokesman Malik Ahmad Khan.
Jamat-ul-Ahrar, a splinter group of Pakistan's Tehreek-i Taliban (TTP) -- also known as the Pakistani Taliban -- claimed responsibility for that attack in a statement emailed to CNN.
CNN's Sophia Saifi and Adeel Raja reported from Islamabad and Laura Smith-Spark wrote from London. CNN's Ray Sanchez and journalist Saleem Mehsud contributed to this report.