In late March, the ministry ordered the slaughter of about 22,000 cows in a bid to control the spread of the disease. So far, 8,000 have been culled.
An MPI spokesperson said the ministry expects the majority of the culling to be finished by the end of this month.
"It may, however, not be completed on some properties until June or July as we are working to accommodate the circumstances of the individuals impacted by the cull," the MPI spokesperson said.
The meat from the culled cattle can be consumed because the disease does not infect humans and presents no safety risk.
Economists have said the culling is a very small portion of the overall slaughter that takes place annually.
New Zealand's total dairy cattle population is about 6.5million, with 5million producing milk. Farmers tend to cull about 20% of their herds each season under normal circumstances. The latest data from Stats New Zealand shows 1.06million adult dairy cattle were slaughtered in the year to March 2018.
As a result, the cull is unlikely to have a material impact on meat prices or milk production, said Bank of New Zealand senior economist Doug Steel.
MPI has consistently said it aims to eradicate the disease from New Zealand but "a final decision on how it should be managed in future has yet to be made," the ministry spokesperson said.
"Our recent decision to cull cattle on infected farms was to help preserve options - it was not the start of eradication. So far it has been in New Zealand's interest to contain the disease and to track its spread to give us the best options for the future, which could be to attempt to eradicate or move to long-term management," the spokesperson said.