The shootings took place in Kerani, a neighbourhood on the outskirts of Quetta, when police stopped two suspected militants on a motorcycle, senior police official Zahoor Afridi told AFP.
"When policemen stopped them, the gunmen on motorcycle opened fire. One of the suspects was killed, while the other was wounded but he managed to escape," Afridi said.
A female passer-by and her daughter were wounded in the shootout. As police were taking them to hospital, another gunmen fired at them and killed two policemen and the wounded woman, Afridi said.
Afridi said the dead suspect had been identified but did not name him. He said his brother was wanted for several sectarian murders.
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Sectarian violence - in particular by Sunni hardliners against the Shiites who make up roughly 20 per cent of Pakistan's 200 million people - has claimed thousands of lives in the country over the past decade.
The worst atrocities have occurred in the southwestern province of Baluchistan, of which Quetta is the capital. It is home to some 200,000 Shiites, according to local organisations.
Baluchistan is also home to a long-running nationalist insurgency aimed at seeking greater control over the province's rich oil, gas and mineral resources.