"This is a man who has had a controversial past but in recent months he has become a very prominent figure, even meeting George Bush," Al Jazeera's James Bays said.
Sheikh Risha had urged the tribal leaders in other Iraqi provinces to follow al-Anbar's lead in co-operating with the central government against al-Qaeda.
"He was returning home when his convoy was hit by a roadside bomb planted by insurgents," Colonel Tareq al-Dulaimi, al-Anbar security chief said.
"His car was hit directly."
Sheikh Jubeir Rashid, a senior member of Abu Risha's group, told the Associated Press:
"It is a major blow to the council, but we are determined to strike back and continue our work. "Such an attack was expected, but it will not deter us."
Two of Risha's bodyguards were also killed by the roadside bomb, Colonel Tareq Youssef, supervisor of Anbar police, said.
Police announced a state of emergency in Ramadi after the bombing and set up additional checkpoints throughout the city, Rashid said.