The ministry said there were more than 15 active as at this month and extracting the information would require substantial work.
MPI also refused to say how many are former police officers reporting to the response team.
The OIA request was made against a backdrop of long-standing cattle farmer frustration and distress over MPI's handling and day-to-day contact with ministry representatives in the M. bovis disease eradication effort.
That has to date seen 32,561 animals from 30 farms slaughtered, the majority, farmers say, showing no signs of the bacterial disease.
Farmers report a "huge disconnect between MPI and people on the ground," said Federated Farmers national dairy chairman Chris Lewis.
"They feel they're dealing with bureaucrats. It takes five or six decision-makers to sign off on something. When you're dealing with animals and feed, quick decisions are crucial."
Lewis acknowledges leadership teams need some expertise not directly related to the focus subject, but in biosecurity he would expect "some dirt under the fingernails" experience.
"You'd expect some to show affinity to the land, some connection. The feedback is that some (MPI) decisions around M. bovis have perplexed. They haven't come from common-sense agriculture experience.
"There are some awesome people in MPI. But MPI would be more awesome if there was some connection with agriculture."
Former MPI director general Wayne McNee, who oversaw the merger of the former Ministries of Agriculture and Fisheries to become MPI, declined to comment on the OIA response.
MPI director human resources Erina Clayton disagreed with the Herald's contention that the lack of direct background and qualifications in agriculture or science for all but two of MPI's senior leadership team — both currently in roles not immediately connected to biosecurity — was a serious deficiency.
"All of the individuals on MPI's senior leadership team have backgrounds that qualify them for the positions they hold as organisational leaders and decision-makers. In addition SLT members receive advice from a range of expert employees.
"MPI also engages and consults with experts from a wide range of fields, including agricultural and biological science experts, across all its activities spanning primary production, biosecurity, food safety, animal welfare, fisheries and trade."
Scientist and former AgResearch chief executive Dr Andrew West, whose field of expertise is ecology and micro-organisms, declined to comment on MPI's biosecurity leaders' credentials but said science was "critically important" in the context of biosecurity.
"You've got to treat this almost in a military manner. This is defence. You have to ask yourself some very serious questions about how you populate an aspect of this defence — what you need inside the core entity.
"But what is absolutely crucial, no matter how you structure it, is the quality and depth of relationships you have with the scientific community and that involves universities and Crown research institutes.
"Science always has to have complete involvement in the planning scenario. It's fundamental. The biggest risk that any primary industry faces in this country is biosecurity."
Asked to comment, Minister of Agriculture and Biosecurity Damien O'Connor said in a statement: "It's for the Director-General (of MPI) to ensure the ministry's staff have the right skills and best knowledge to carry out their duties and to link up with other groups as needed".
Economist Peter Fraser, a former ministry policy leader, said "professional managers" were valuable and necessary in government departments.
"You don't want departments run by economists or scientists. But it's essential that the expertise of that organisation is reflected in the organisation in other ways."
The alternative to the Government's "one-shot" eradication attempt, which is forecast to require the killing of about 150,000 cattle over two years, was management of the disease as it occurred. It is endemic in the world's dairying herds.
Affected farmers are entitled to compensation for their slaughtered cattle. For most farmers, the edict has meant their livelihoods disappeared overnight. Those whose properties have been in a Government lockdown and unable to move cattle have incurred large feed costs.
A common complaint, acknowledged as justified by Agriculture Minister Damien O'Connor, has been MPI's slowness to pay out on claims.
