The 10-year-old, who is second in line to the throne, was on holiday with her parents King Willem Alexander and Queen Maxima when the accident happened.
"She was immediately taken to hospital by helicopter where a fracture was found in her right thigh," the palace said in a statement.
"She is being operated on."
The Dutch royal family visit the exclusive ski resort of Lech in western Austria every year, having holidayed there since the late 1950s.
It is not the first accident to befall the royal family in Lech.
King Willem's younger brother Friso died from injuries sustained in a skiing accident.
Friso was caught in an avalanche near Lech in February 2012 and buried for some 20 minutes under the snow, leaving the 44-year-old prince comatose and brain-damaged. He died in August 2013.
Alexia is the second daughter of the king and queen. Her 12-year-old sister Catharina-Amalia, the Princess of Orange, is the heir apparent to the Dutch throne. They have a younger sister, Princess Ariane, who is eight.