About 11.15pm on Friday a car entered the church grounds from Moray Pl.
It stopped and then suddenly reversed, crashing into the wall, damaging a 2.5m section and an elaborate gate support tower. The car was then driven off.
Police are investigating after a taxi driver was able to supply details of the car.
Church caretaker Malcolm West said security-camera footage showed there appeared to be four people in the car.
Unfortunately, a van belonging to Presbyterian Support skidded on ice in the driveway on Monday and collided with the wall in the same spot, he said.
A section of retaining wall with a bluestone facade and two capping blocks made of Port Chalmers breccia were damaged in the crashes.
The gate support tower was leaning and had turned slightly on its base.
Mr West did not know how much repairs would cost, but the last time the gate support tower was damaged (also in a crash) it had to be lifted and turned, costing "thousands".
The remedial work would be done in conjunction with the Historic Places Trust, he said.
