The planting day, which aims to help people engage with nature, was scheduled to take place on Saturday.
Due to Auckland moving into Alert Level 3 conditions last week, ANZ staff and equipment needed for the plantings have been unable to make the journey down south.
Close to 200 school students were scheduled to help plant trees in the same area on Wednesday, but that has also been postponed.
Sustainable Coastlines Programs manager Dan Downing said the Waimakariri River was an important asset to the city and it was a shame the planting days had been postponed.
He said planting trees along the Waimakariri would helped stabilise the river's banks, create habitat for animals, reduce sediment loss, soak up excess nutrients of phosphorus nitrate and decrease carbon from the atmosphere.
Last year Sustainable Coastlines planted more than 60,000 trees however. This year's goal of 30,000 was under threat due to Covid-19, Downing said.
Next year the organisation planned to work with farmers to find more land to plant on.