Ms Zaitseva's armed bodyguards reportedly drove up in two jeeps immediately after the crash and protected her from a furious crowd who witnessed the appalling crash.
One onlooker who was trying to help the injured described the scene as being like "a war zone."
The driver of the Touareg, Gennady Dronov, 49, was on a green light when the vehicles collided, witnesses said.
Ms Zaitseva, daughter of local energy company multi-millionaire Vasily Zaitsev, was uninjured.
A shocking video of the aftermath of the crash showed bodies strewn on the pavement.
Student Ms Zaitseva was detained initially for three days. Police said she was found not to have been drinking before the crash.
If charged and convicted of causing the crash, she faces up to 10 years in jail.