The attack was carried out by two men on a motorcycle while the school in Baldia Ittehad town of was conducting a ceremony to announce examination results, police said.
Principal Abdur Rasheed, a member of the Awami National Party, succumbed to his injuries at a hospital.
The injured children, aged between five and ten are being treated at the Civil hospital.
"A large number of children were present when two men on a motorcycle came and hurled a hand grenade at the building," a senior police official said.
Eyewitnesses told a news channel that the two men barged into the school and hurled another hand grenade. They also opened fire inside the school.
Rasheed held a senior position in the party and was reportedly receiving threats over not paying extortion.
A fellow ANP leader Syed Waheed was seriously wounded in the attack, police said.
Police and paramilitary personnel surrounded the area and launched a search operation soon after the attack.
No group has yet claimed responsibility for the attack, which police said was apparently linked to political rivalry.
The southern port city saw some violence yesterday as well, when unknown assailants killed seven people in the city including two traffic wardens in Nazimabad and a police Sub-Inspector in Lyari.
SP Khurrum Waris said the traffic wardens were returning home after performing their duties when gunmen on motorcycles opened fire on them near board office.
"One of them died on the spot while another passed away in hospital," he said.