The broken part is a stainless fitting joining the two main royal backstays, supporting the top-most part of the main mast.
There was no immediate danger to the ship or any of the 46 people on board.
Captain Phillips expected to arrive at Opua on Friday morning. The damaged part would be removed and a ship yard in Whangarei would be asked to make a new one.
The Canadian ship Picton Castle pulled out several days ago, which leaves just five vessels in the race. It is also continuing under motor.
The crews will be welcomed with a powhiri at Russell's Haratu Marae at 4pm on Saturday. Europa and Lord Nelson will be open to the public from 1-4pm at Opua wharf on Sunday.