Authorities destroyed the first batch by burning elephant tusks and carved ivory figurines and bracelets in a rotary kiln.
Destroying the 28-ton stockpile, which is one of the world's largest, is expected to take until mid-2015.
The ash left after incineration will be mixed with cement and lime and dumped in landfill. About 1.6 tons of ivory will be kept for educational or scientific purposes.
The destruction follows similar initiatives in the past year by Belgium, France, China, the US and the Philippines.
Hong Kong's stockpile has grown after customs agents intercepted a series of big shipments of smuggled ivory in recent years.