The attacker targeted a crowd that had gathered as the body of a prominent lawyer murdered earlier on Monday, Bilal Kasi, was being brought in.
Lawyers and journalists were among the dead. About 120 people were injured.
The Taliban faction, Jamaat-ul-Ahrar, said it was behind both the hospital attack and the killing of Mr Kasi.
He was head of the Balochistan province bar association. He was shot while on his way to the court complex in Quetta.
Jamaat-ul-Ahrar [The Party of Freedom Fighters] split from the Pakistani Taliban two years ago.
It has claimed a number of major attacks, including a suicide bombing that killed more than 70 people - including many children - at a park during Easter celebrations this year.
Balochistan, Pakistan's poorest province, has long been plagued by insurgency.
A number of people, including lawyers, have been murdered in Quetta in recent weeks.
Mr Kasi had strongly condemned those attacks. He had announced a two-day boycott of court sessions in protest at the killing of a colleague last week.
After the hospital blast, Pakistani Prime Minister Nawaz Sharif and chief of army staff Gen Raheel Sharif both went to Quetta for talks with security officials.
Mr Sharif expressed his "deep grief and anguish", adding: "No-one will be allowed to disturb the peace of the province. The people, policy and security forces in Balochistan have given sacrifices for the country."
The president of Pakistan's Supreme Court Bar Association, Syed Ali Zafa, called the assault "an attack on justice". The Pakistan Bar Council has announced a nationwide strike by lawyers on Tuesday.
Those killed in the hospital attack were said to include Baz Muhammad Kakar, a predecessor of Mr Kasi as provincial bar president, and more than 30 other lawyers.
Two journalists have also been identified among the dead - Shahzad Khan, a cameraman for Aaj TV, and Mehmood Khan, a cameraman for DawnNews.
Lawyers in Lahore staged a demonstration to condemn the attack. Some journalists also protested, demanding protection for freedom of expression.
A faction of the Pakistani Taliban has said it carried out a suicide bombing that killed at least 70 people at a hospital in the city of Quetta.