A2 Milk says it will vigorously defend the proceeding.
The liquidator of the Porirua company said there appeared to be no assets in the business with new funds being used to pay previous investors.
Infratil has already enjoyed considerable success in investing in data centres following its 2016 purchase of a stake in Canberra-based CDC Data Centres.
New Zealand airports could well lose out in a "race for capacity" as airlines shift their aircraft into other, profitable markets.