A 13-year-old girl has been arrested after allegedly throwing a trolley over a railing at a shopping centre and injuring a man below.

The incident occurred at the Victoria Avenue centre in Chatswood, on Sydney's lower north shore, at 11.50am on Monday.

A 59-year-old man had been walking on the ground floor when the shopping trolley struck him from above.

Paramedics treated the man for head and facial injuries before rushing him to Royal North Shore Hospital in a stable condition.

The 13-year-old girl was taken to Chatswood Police Station, where she assisted police with their inquiries.