"With regard to dairy products, one farm has been identified as having fed contaminated feed to dairy cattle," he said.
"All milk from this farm has been prevented from entering the food chain."
Mr McGimpsey said the results of tests on carcasses of cattle thought to have been given the feed were expected at the end of the week.
Agriculture Minister Michelle Gildernew said the cattle herds which received the contaminated feed had been restricted and could not enter the food chain.
Mrs Gildernew said she was first made aware of the issue on Saturday evening, while her department found out on Friday.
The minister insisted the temporary withdrawal of Northern Ireland pork from shops on Monday was not an over-reaction.
"We did act prudently and in a measured fashion in order to ensure consumer confidence and in order to ensure the viability and sustainability of our farming industry - which is a very important industry to the economy here and one we want to protect," she said.
'No beef recall'
In the Republic of Ireland, tests on beef herds which ate contaminated animal feed have come back positive but officials say there is no risk to public health.
A news conference in Dublin, organised by the Food Safety Authority and the Department of Agriculture, heard that out of 11 herds tested, three were "technically non-complaint".
There is to be no public recall of beef.
The Irish government said it would take three measures: any animals in herds above the legal limit will be taken out of the food and animal feed chain; any products from these animals will not be released into the market; and the European Commission will be informed of the results.
Animals from 34 other herds are currently restricted.
The Irish Food Safety Authority said if tests come back within acceptable limits those animals would be released into the food chain.
If they are unacceptable, the animals would not be released.
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