In the first attack in Kano four polio vaccinators were shot dead by gunmen who drove up on a motor tricycle.
Thirty minutes later gunmen opened fire on women waiting with their children in Hotoro, outside Kano city.
In 2003, northern Nigeria’s Muslim leaders opposed polio vaccinations, claiming they could cause infertility.
Kano banned motorbikes from carrying passengers after a recent attack on the prominent Muslim leader, the emir of Kano.
Residents told the BBC’s Yusuf Yakasai in Kano that those injured in the shooting at the health centre there had been taken to hospital.
It is not clear if health workers were among the casualties in Hotoro, where gunmen also approached using a motor tricycle.
Analysts believe the attack last month on the emir of Kano may have been the work of the militant Islamist group Boko Haram.
The group – whose name translates as “Western education is forbidden” – says it is fighting to overthrow the government and impose Sharia.
It has been blamed for the deaths of some 1,400 people in central and northern Nigeria since 2010.
Nigeria is one of only three countries where polio is still endemic.