The attack injured about 50 people, who were taken to Jinnah hospital.
About an hour later there was a large blast just outside the emergency ward of the hospital.
The BBC's Jaffer Rizvi, who was at the scene at the time, said there was a huge panic inside the hospital. Hundreds of people mourning those killed in the first attack had gathered there and were shouting slogans condemning both militants and the government.
Police officer Ghulam Nabi also told Reuters news agency another bomb had been defused after being discovered inside a TV set on the hospital premises.
The Shia community in Karachi has declared that Saturday will be a day of mourning.
Sectarian tension between the Shia minority and the Sunni majority rose after the December attack, and riots erupted.
Tension remains high, and paramilitary troops were deployed in the city days ago amid deadly clashes between rival political groups.
The Shia-Sunni schism originates from a dispute soon after the death of the Prophet Muhammad over who should lead the Muslims.
Sunnis remain the majority globally, with Shias estimated to number about 10% of all Muslims.
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