The blasts occurred as a Rangers convoy was coming out of the headquarters on Miro Khan road in Larkana city.
The explosives were planted in a bicycle and in a garbage bin close to the headquarters, police officials said.
"The twin blasts left four Rangers officials injured and one of them later passed away in hospital," police official Qadir Nizamani said.
He said 12 other civilians who were passing by the headquarters were also injured in the blasts and taken to hospital for treatment.
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Hours after the attack, Ahsanullah Ahsan, a spokesman for the Jamaat-ul-Ahrar militant group, claimed responsibility in a statement, in which he warned of more such attacks in the future.
Larkana was the site of a standoff between the Rangers and the Sindh government and local police earlier this month when the paramilitary force raided government offices to arrest a high-profile member of the Pakistan Peoples' Party, Asad Kharal and his relative Tariq Kharal.
The Rangers later said that Larkana police had helped Kharal escape although he was wanted in corruption cases.
The Rangers and National Accountability Bureau (NAB) officials wanted to question Kharal about his alleged role in two corruption cases involving 500 million rupees.
In apparent retaliation, the Rangers raided the home of outgoing home minister Anwar Siyal in Larkana and later Asad was arrested from Hyderabad.
Earlier this week, two military personnel belonging to the intelligence wing were shot dead in Karachi in a target killing in the busy Saddar area.
Taliban had claimed responsibility for the attack.
Shah replaced Syed Qaim Ali Shah and faces a tough challenge of managing law and order in the province.