The New Zealand Historic Places Trust says the Timeball Station in Lyttelton that was badly damaged in the earthquake will have to be demolished.
The building is one of many Category 1 and 2 listed buildings to have suffered extensive damage in the 6.3-magnitude quake on 22 February.
Listed as Category 1, it is considered internationally significant because of its maritime history.
An example of Victorian technology, the Timeball Station is one of only five in the world known to be still in working order.
From 1876 to 1934 a ball dropped from the mast on its stone tower, signalling the time to ships in the harbour, the trust's website says.
Visual time signals were necessary to correct ships' chronometers and ensure accurate navigation.
Use of the timeball was discontinued in 1934 when it was replaced by radio signals.
Historic Places Trust chief executive Bruce Chapman says engineering checks have revealed the building is too dangerous to save and it will have to come down.
He says the decision has been taken with enormous regret, but public safety is paramount.
Mr Chapman hopes it will be possible to recover the timeball mechanism itself, and the trust will look at options for reconstruction.
He says the aim is to restore some of its significance to the local community.