The fire started at a furniture store and quickly engulfed other shops on the ground floor of the building known as Ayesha Manzil, said Karachi Mayor Murtaza Wahab.
Earlier this week, city planners and engineers said they were sure that most structures in Karachi, residential, commercial and industrial, did not have fire prevention and firefighting systems.
In the first incident, 11 labourers were injured when the roof of a two-storey garment factory collapsed in the Korangi industrial area of Karachi city.
CCTV footage shows the suspect was wearing a mask to conceal his identity and that the motorcycle he was riding did not have a number plate.
Powerful winds and storm surges were forecast to hammer a 325-kilometre (200-mile) stretch of coast between Mandvi in India's Gujarat state and Karachi in Pakistan.
It was 840 km away from the port city of Karachi and was heading towards the coastal areas of Sindh and Balochistan provinces.