The most common tort claim is one for alleged negligence.
Justice Brown's decision also goes into more detail on the application Fonterra has launched to try suspend Danone's court action.
This relates to international arbitration which began in Singapore last month involving companies in the Fonterra group and Danone.
The Fonterra companies in this arbitration do not include Fonterra Co-operative Group, which is the specific defendant Danone is suing in New Zealand.
"Nevertheless the defendant has made application to this court for an order staying the current proceeding pending the final determination of arbitration proceeding," the judge said.
Justice Brown said the media's application to view the court documents could be revisited once Fonterra's bid to suspend the court claim has been determined.
Fonterra wrongly suspected in August last year that 38 tonnes of whey protein - used to make products including infant formula manufactured by Nutricia - had been contaminated with a botulism-causing bacterium. The whey protein was ultimately cleared but not before a recall of baby formula products amid fears that children could be harmed.
Nutricia had to recall 67,000 cans of its Karicare baby milk brand in New Zealand. Of the eight customers affected by Fonterra's recall, the company agreed to a commercial outcome with all of them except Danone.