The Stoke Memorial Hall, The Refinery and the Hounsell Circle Bus Shelter will be closed to the public by the end of the month.
The council says none of the buildings pose any immediate danger to the community.
But it says the buildings are all quake-prone, and the council is not prepared to accept the level of risk they present should an earthquake occur.
The council is working to find a new home for the Nelson Arts Council, which is currently based in The Refinery.
