According to Karachi police, six gunmen on motorcycles, appearing to be from a banned extremist group, stopped the bus and fired indiscriminately.
The bus carrying about 60 was going to an Ismaili Shia place of worship.
Shia minority are the target of frequent sectarian attacks from Sunni militant groups.
No group has yet said it carried out the attack.
Provincial police chief Ghulam Haider Jamali said the attack appeared to be the work of the same group involved in recent drive-by shootings of senior police officials in Karachi.
Ghulam Haider Jamali said the bus was on its way to an Ismaili Shia Muslim place of worship when gunmen boarded it in the Safoora Goth area of Karachi and fired at those on board.
The attackers are said to have escaped easily.
The Taliban and other Sunni Muslim extremist groups have targeted Shia Muslims in Pakistan in the past.
In the last few months, several mosques belonging to religious minorities have been bombed.
Pakistan is about 20% Shia and 70% Sunni. Ismaili Shias, in common with other Shia Muslims revere Ali, son-in-law of the Prophet Mohammed.
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