One rocket hit a shop in a busy market in Quetta, the capital of Balochistan province, killing one person and injuring 18 others, they said.
The Qandahari market was crowded with shoppers when the rocket landed there, creating panic among people.
The second rocket hit Basti Panchayat, a Christian neighbourhood, and injured three persons, local residents and police said.
The injured were taken to two nearby hospitals.
Traders closed their shops and security forces cordoned off the site of the attacks.
The rockets damaged several shops and buildings, witnesses said.
No group claimed responsibility for the attacks and police were not aware of the location from where the rockets were fired.