The Waymo vehicle was hit when a Honda sedan swerved to avoid another car and drove into the opposing traffic lane.
Police in Chandler, Arizona, said the Waymo car was in autonomous mode, although there was an occupant in the driver’s seat.
A video released by Waymo shows how the oncoming sedan swerves across multiple lanes before the crash.
Questions will be raised regarding whether a human driver would have been able to move out of the Honda’s way.
Waymo said: “Our team’s mission is to make our roads safer – it is at the core of everything we do and motivates every member of our team.
“We are concerned about the well-being and safety of our test driver and wish her a full recovery.”
A spokesperson for Chandler Police said that the department did not regard the autonomous vehicle to be at fault for the collision, and neither Waymo nor the car’s driver would be cited.
In March, Waymo announced that it had purchased 20,000 electric Jaguar cars in a deal estimated to have been worth $1.4bn (£990m).
At the time, the company’s chief executive John Krafcik said: “We have been working on this at Google and now as Waymo for over nine years, nearly a decade.
“We do like to consider it the world’s longest ongoing driving test. And we’ve spent so much time focused on making sure this technology is right.”
Mr Krafcik said that the company has conducted five million miles of road testing on top of five billion miles of simulation testing, putting the cars in 20,000 different scenarios to ensure the technology is safe.
The safety of self-driving cars is of concern to many regulators.
Uber suspended testing its autonomous vehicles after one struck and killed a female cyclist in March.
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Investigators said the vehicle was in autonomous mode with an operator behind the wheel when Elaine Herzberg was struck.
The 49-year-old woman, who had been walking her bike when she was hit by the car, died from her injuries in hospital.