"Self-driving cars will likely force auto insurers to rethink their business models," the report said, while noting "widespread adoption of this technology is decades away."
However, the building blocks of self-driving cars, including features such as automatic braking, adaptive cruise control and lane-departure warning, are already rolling out onto many vehicles.
These accident-avoidance technologies are likely to have an "immediate" effect on insurance premiums.
"Auto insurers will face higher auto repair costs from embedded cameras and sensors which are often located in or near bumpers," the report said.
"Widespread adoption of self-driving cars is still decades off, but it raises questions of what an auto insurer's role will be in a world with far fewer accidents," the report said. "Regulators, lawmakers and courts will have to determine how liabilities are shared among insurers, automobile manufacturers and technology companies."
Edmunds says: Self-driving cars are on the road to shaking up the automotive landscape, from how we drive to how much we pay for car insurance.