Mr Groser has described the situation as "very serious". The Government is likely to raise its concerns about the way Fonterra has dealt with the issue, and set out what it expects the company to do from here.
Russia has reportedly banned all Fonterra products.
The issue has the potential to cause major damage to New Zealand's reputation for food safety with trading partners, including China.
The Shanghai Daily, the Voice of China, Nongmin Ribao (the Farmers' Daily), Xinhua, and the People's Daily all featured stories prominently today.
Authorities have recalled up to 1000 tonnes of dairy products across New Zealand and seven other countries after Fonterra announced tests had found a bacterium that could cause botulism.
The Ministry of Primary Industries said yesterday the tainted products included infant formula, sports drinks, protein drinks and other beverages. Countries affected beside New Zealand included China, Australia, Thailand, Malaysia, Vietnam and Saudi Arabia.
The botulism bacteria scare is likely to cause "sheer, absolute panic" in China as the news filters through the world's second biggest economy, says a Kiwi involved in the dairy trade.
Gregg Wycherley, managing director of Auckland baby milk brand Fresco Nutrition, said he anticipates "wholesale removal of New Zealand infant formula off Chinese supermarket shelves" by tomorrow morning.
"News of the contamination will just go viral in the Chinese social media," he said.
Trade Minister Tim Grosser said Fonterra's botulism scare was "very serious" and it was "absolutely appropriate" that China had stopped all imports of New Zealand milk powder.
Speaking on TVNZ's Q+A programme, Mr Grosser said he would head to China "at the drop of a hat" if he received advise that political contact would be useful.
"The authorities in China, in my opinion, absolutely appropriately have stopped all imports of New Zealand milk powders from Australia and New Zealand."
He was focused on dealing with the immediate problem of the wellbeing of users of the products.
"Today our sole concern is on the health of infants and other users of these products, both our own and in the countries' that we're exporting to. So it's not that we don't think there's some very important questions, but we're focusing on the essential problem of today.
"We don't want Fonterra worrying about their long-term reputation or risks right now. We want everybody focused on the health of the little babies."
Weibo, a Chinese social networking website similar to Twitter, was starting to buzz with talk of the potential contamination last night.
Many users were pointing out Fonterra's links to Sanlu, one of the companies responsible for China's 2008 melamine scandal, in which at least six babies died and thousands more became sick after consuming dairy products.
Fonterra yesterday announced three batches of a whey protein called WPC80, manufactured in May last year, may have been contaminated by a dirty pipe at the company's Hautapu plant, in the Waikato.
The dairy co-operative said eight of its customers, most of whom have still not been named, may have used the affected batches in a range of products including infant formula and sports drinks.
The Centres for Disease Control describes botulism as a rare but sometimes fatal paralytic illness caused by a nerve toxin.
Infant formula manufacturer Nutricia has instigated a precautionary recall in New zealand of its Karicare Infant Formula Stage 1 (0 - 6 months) in New Zealand only with batch numbers 3169 and 3170 (use by 17.06.2016 and 18.06. 2016).
It has also recalled its Karicare Gold+ Follow On Formula Stage 2 (6-12 months) in New Zealand only with batch number D3183 (use by 31.12.2014).
"Nutricia's quality and food safety management system includes rigorous testing procedures of our finished products," the company said in a statement.
"None of the products tested and sold in New Zealand indicate any contamination. However, given the new information supplied by Fonterra, we have taken the decision to make a precautionary recall on specific products."
New Zealand's reputation for high-quality food products - the driving force behind some $2 billion in annual dairy exports to China - also took a hit in January when traces of dicyandiamide, a nitrate inhibitor, were found in New Zealand milk.
Fonterra chief executive Theo Spierings was flying from Europe to China yesterday.
China's import authority yesterday ordered an immediate recall of any products containing the affected batches of Fonterra WPC80, the state-run news agency Xinhua said.
Simon Page, managing director of infant formula exporter BioPure Health, said it was a bad look for Fonterra and New Zealand to have two contamination scares in less than eight months.
"Something's not right," he said.
