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.
Image source: Wikimedia Commons President-elect Donald Trump celebrated his election victory at the Ultimate Fighting…
Millions of voters across the US chose to return Donald Trump to the White House…
Donald Trump declares victory in the US election as he addresses jubilant supporters in Florida.…
Stocks around the world are rising as Donald Trump appears to be on the cusp…
Donald Trump has won Pennsylvania, North Carolina and Georgia and taken a lead over Kamala…
Quincy Jones, the celebrated musician and producer who worked with Michael Jackson, Frank Sinatra, Ray…