The Duke and Duchess have been in contact with the woman, Kensington Palace said, after she had been hospitalized after an incident with a police engine who participated in the convoy.
The couple were on their way to Windsor for a chapel service when the event occurred in Richmond, West London, Monday afternoon.
"At around 12: 50h on Monday, June 17th, a strange police motorcycle was involved in a collision with a pedestrian on Upper Richmond Road, Richmond," London Metropolitan Police said in a statement.
"The woman, believed to be in the 80s, has Her nearest family has been informed, the statement said.
Kensington Palace said: "The Duke and Duchess of Cambridge were deeply concerned and sorry to hear about the accident on Monday afternoon. "
" Their royal highs have sent their very best greetings to Irene and her family and will keep in touch during all stages of her recovery, "added the palace.