A senior police official in the western city told the BBC the device was planted on the roof of the vehicle.
The blast comes at a time of relatively diminished violence in Pakistan. No-one has said they carried out the attack.
Balochistan province suffers from separatist, sectarian and Islamist insurgencies.
There is a heightened alert against sectarian attacks in the region, as it is the Shia month of mourning.
Reports suggested the passenger bus was carrying workers from the centre of Quetta to their homes in the suburbs at the end of the working day.
"This is a cowardly act that has targeted innocent people," the provincial Interior Minister Sarfaraz Ahmed Bugti told Reuters news agency.
"We are fighting against terrorism here. And we will keep fighting until the last terrorist is killed."
A bomb explosion on a bus in the Pakistani city of Quetta has killed at least 11 people and wounded a further 22, police say.