Canterbury Civil Defence has issued an urgent warning for Towy River, a tributary of the Conway River, with a dam in danger of overflowing.
The dam was formed by slips caused by last week's magnitude 7.8 earthquake.
People are being urged to stay out of the water and away from the rivers.
The agency said a rapid rise in the water level was likely.
Urgent warning – Conway River! Stay out of the river bed and well away from the river as there is danger for a rapid water level rise.— Canterbury CDEMGroup (@CanterburyEM) November 22, 2016
View RNZ's full coverage of the earthquakes here.