The blast occurred at around 10am (0700 GMT) near the offices of the Anbar provincial government, and also left 35 people wounded, according to police Major Rahim Zabin and a doctor at Ramadi hospital.
"A suicide car bomb targeted a police checkpoint in the centre of the city, about 200 metres from the Anbar government offices," Zabin said.
"He killed eight people, including six policemen and one woman."
A doctor at Ramadi hospital, who spoke on condition of anonymity, confirmed the death toll, and said medics had so far treated 35 people for injuries, including women and children.
Ramadi lies 100 kilometres (60 miles) west of Baghdad and is the capital of predominantly Sunni Arab Anbar province, Iraq's biggest by area.