Maritime New Zealand said it expected waves of up to eight metres to batter the wreck.
Salvage barge the Smit Borneo had left the wreck due to poor conditions and was likely to remain in port until Sunday, it said.
"The wreck remains in a fragile state and will continue to deteriorate the longer it remains exposed to the elements. The forecast bad weather may result in further damage or movement of the wreck, along with the potential loss of more containers or container debris."
There are still 685 containers on board the Rena, which crashed into the Astrolabe Reef off Tauranga last year.