Police said the accident occurred around 11:50am, and the motorcyclist died at the scene, on the northern side of the bridge near Glenavy.
Senior Sergeant Jason McCoy, of Oamaru, said the crash involved three motorcycles and another vehicle.
The bridge - State Highway 1 - is closed and motorists are being diverted up the Waitaki Valley to cross the river at the Kurow-Hakataramea bridge.
Motorists are advised to avoid the area If possible.
An Otago Daily Times reporter at the scene said truck drivers on the southern side of the bridge expected the highway to be closed "for hours".
The Serious Crash Unit is attending and Snr Sgt McCoy said inquiries were continuing.
It is the second fatal motorcycle accident in the South Island over the holiday weekend, after a rider was killed on a rural property near Twizel yesterday.
Today's crash comes on the same day police issued a road warning in which they urged motorcyclists to drive to the conditions.
