Many of the casualties are thought to have been police guarding the clinic.
Armed guards are routine for polio workers in Pakistan, who have been the target of many deadly attacks by Islamist militants in recent years.
Militants oppose polio vaccination, saying it is a Western conspiracy to sterilise Pakistani children.
Pakistan and Afghanistan are the only two countries where the disease is still endemic.
The explosion took place in the morning around the time workers report for duty before heading out on their vaccination rounds, Sarfaraz Bugti, a minister for Balochistan province where the blast took place, told reporters. Around 20 people were injured. Read more on bbc.