Buller Civil Defence said the two containers became dislodged from a property in Murchison in this yesterday's heavy rain.
Its emergency management officer Erica Andrews said one of the containers was currently stuck under a bridge near Murchison.
She said the other container was believed to be heading towards Westport.
Ms Andrews said Civil Defence were currently working to find out what is inside the containers, and how they ended up in the river.
Police have currently closed the Buller Bridge to foot traffic and may be required to close the bridge to road traffic should the container pose a threat to the bridge.
People have been asked to stay away from bridges over the Buller River at this time.