CNN said New Zealand was the world's biggest user of 1080, using about 80 per cent of the world's manufacturing stocks.
The story said Fonterra had been "beset by problems", including the 2013 botulism scare.
Quartz reported that the threat "could have implications far beyond New Zealand's borders because of global fears about contaminated baby formula, especially in China, where 54,000 children were sickened by adulterated milk products in 2008".
The story noted that Fonterra was forced to issue a global recall of formula in 2013, in what turned out to be a false alarm.
China Daily said parents were being reassured that the supply chain was still secure, but that police and food safety officials had failed to identify who issued the threat.