According to the Navy, they won't be berthing, but will receive VIP visitors via helicopter and/or boats.
The task group is expected to depart for Auckland this afternoon.
The foreign ships headed to New Zealand for the Navy's 75th birthday celebrations in Auckland yesterday, but diverted to assist with the post-earthquake response.
Wellington's Harbourmaster has declared a moving exclusion zone around the ships while they are in the harbour.
The exclusion zone extends 500 metres ahead of the ships and 100 metres on either side or behind.
This reduces to 60 metres once the ships are anchored.
The zone will be patrolled by police, Coastguard and the Harbourmaster vessels, and boaties are asked to co-operate with any directions.
As part of the New Zealand Navy's 75th anniversary, the public can get a close up glimpse of international warships during an open day in Auckland today.
Ships from international navies in town for the celebrations are berthed at the Auckland city centre and Devonport Naval Base.
Many of the ships will welcome visitors on board from 10am, including Japan's JDS Takanami and the Republic of Korea's ROKS Chungb.