This means the Service Centre and the Council offices at 101 Wakefield Street will be closed between 2.50pm - 3.30pm. Callers to the Council's 499 4444 phone line will hear a recorded message during the 40-minute period.
If a large earthquake is felt in Wellington, it could quickly be followed by a tsunami - and people in low-lying areas around the inner harbour could be at risk.
Wellington's Civil Defence Controller, Mike Mendonca, says the exercise will be all about "heading up rather than getting out.
"Obviously if a tsunami is on the way, people should head inland or to high ground as quickly as possible. If, however, they are in multi-storey buildings in low-lying areas like the CBD and there's strong shaking then - if the building is still safe - they should not go in to the streets but instead head up.
Mr Mendonca says people should not stop till they get at least above level 2. "The footage from Japan shows how high the water could get if a tsunami surge was to come into the harbour."
On Friday, Council staff and any elected members in the complex will practise the 'drop cover hold' earthquake drill and those who work on the lower floors will move upstairs as if there were a real emergency. The exercise will be overseen by the Council's whistle-wielding emergency floor wardens.
Mayor Celia Wade-Brown, who holds the Council's Emergency Management portfolio, says the Council has placed earthquake resilience and public safety at the top of its priorities.
"The Council's Long Term Plan has identified the need to invest significantly in the safety and resilience of Wellington. Over $44 million has been included in the plan for earthquake strengthening over the next decade, including work on the Town Hall.
"Conducting this exercise reinforces good practice among Council staff so we can get through a major disaster, and in turn help others. We can't compromise safety. Personal and business readiness for disasters is also essential."
Mr Mendonca says the Council, as both a building owner and an employer, is obliged to look after its staff and members of the public who use the Civic Square buildings. "We'll start running these exercises regularly - and it's something that a lot of other corporates and building owners should think about doing too."
The Council will also take part in the Pacific-wide exercise -Operation Shake Out' in September. "This will be another opportunity to test our preparedness and we encourage all Wellington businesses to participate."