The unidentified attackers were on a motorbike and shot dead the policeman deputed to provide security to a polio vaccine team on an immunisation drive in the thickly populated Papoosh Nagar area of the city, police said.
The attackers fled after the shooting.
The vaccination drive remained unaffected by the shooting, officials said.
No one has taken responsibility for the attack so far.
Pakistan is one of only three countries where polio remains endemic, along with Afghanistan and Nigeria.
The militants claim that polio vaccination is a front for espionage or a conspiracy to sterilise Muslims.
So far all efforts to eliminate the the disease have failed. Last year, a record 303 polio cases were recorded in the country.