Irene Mayor, an 83-year-old widow, was on her way home after shopping when she was "clipped" by a mirror on one of the motorcycles that travel with the Duke and Duchess of Cambridge's entourage.
Mayor suffered a number of broken bones, including both arms and her leg, but is said to be in stable condition.
William and Kate, who did not witness the accident, are said to be “deeply concerned and saddened.”
“Their Royal Highnesses have sent their very best wishes to Irene and her family and will stay in touch throughout every stage of her recovery," a spokesman for Kensington Palace said in a statement.
The couple also hope to visit Mayor when she feels up to it.
But Mayor's family is reportedly furious at the motorcycle police escort, whom they accused of driving too fast, according to the Daily Mail.
"My sister is lying in a hospital bed and she could have been killed. She could so easily have been killed," said Mayor's sister, Joyce Shore.
Her brother, who asked not to be identified, said he has met with lawyers regarding the incident. However, he added that he doesn't blame the British royals.
"It could happen to anybody. I understand the movement of the police and the reason they have these convoys," he told the Mail.
The Metropolitan Police will investigate what exactly happened.