"We have the farm in question under lockdown and we are doing further testing," Guy said.
"The farmer is co-operating very closely with MPI. I think that what we need now is calm heads as we work our way through it," he said.
The disease spreads from animal to animal, unlike the far more serious disease, foot and mouth, which is windborne.
Guy reiterated the ministry's view that the outbreak did not represent a food safety issue.
"It's not going to affect our international trade and we don't believe that it will, because all of the countries that we trade with have already got it," he said.
Guy said he hoped that the disease could be eradicated in New Zealand.
At a low level, he said the outbreak could affect animal production, as has been the case overseas.
Dairy NZ chief executive Tim Mackle appealed for calm. "There's no reason to push the panic button," Mackle said. "We have got to remain calm and work our way through it," he said.
News of the outbreak caused a minor and temporary dip in the New Zealand dollar on Tuesday.
ASB rural economist Nathan Penny said he was keeping a "watching brief", particularly if the outbreak becomes more widespread.
"Based on what we know to date, this appears to be at the 'not very serious' end of the scale," he said.
"In particular, it's not a food-safety risk and MPI appear to have it contained," he said.
"Also, this falls into the 'managed disease' category, with most of our competitors already having it," he said.
Waitaki MP Jacqui Dean said the disease was detected on a Glenavy farm and it was not only disappointing but also concerning for other farmers in the region who were "just getting back on their feet" after last week's floods.
MPI has put legal restrictions in place to stop any movement of stock from the property while the scale of infection is determined.
MPI was advised of sick cattle at the property last Monday and mycoplasma bovis was confirmed by the Ministry's Animal Health Laboratory late on Saturday.
"Fourteen cows have tested positive for mycoplasma bovis and approximately 150 cows on the property have clinical signs that indicate they may be affected. MPI is now tracing movements of animals on and off the property to ascertain if other properties are at risk," the Ministry's Director of Response, Geoff Gwyn, said.
"Right now, we do not know when or how the disease entered New Zealand," he said.
Farmers have been were advised to contact their vet if stock showed unusual levels of mastitis or abortions, or presented with arthritis or pneumonia.
New Zealand First said the outbreak represented another breach of biosecurity and said Guy should be held accountable.
"Of real concern is how mycoplasma bovis got here," NZ First leader Winston Peters said in a statement.
Since 2008, Peters said there had been well over 150 post border incursions and since 2016 alone, including velvet leaf, pea weevil and myrtle rust.
