George Eustice told the Commons that the Government will issue new guidance to plants to try to stop further spread.
A meat processing site owned by Asda in Cleckheaton last week became the third food plant in 48 hours to confirm an outbreak after about 150 workers fell ill with the virus. The Kober plant, which supplies bacon to Asda supermarkets and employs more than 500 people, has closed until this week with a test-and-trace programme under way.
Three workers also died from coronavirus after a small outbreak at a meat processing plant in Barnsley last month. Eleven workers were diagnosed with the virus and seven were hospitalised at Cranswick Convenience Foods in Wombwell.
On Tuesday, Prime Minister Boris Johnson said the Government is investigating the cause, while chief scientific adviser Sir Patrick Vallance said the cold environment in such factories could be a factor.
In Germany, Europe's largest meat processing plant suffered a Covid-19 outbreak which resulted in approximately 7,000 people being quarantined.
During Environment Questions, Labour's Luke Pollard asked whether statutory sick pay is high enough to ensure people do not feel compelled to work even if they are ill.
Responding, Mr Eustice said: "We have had now three outbreaks linked to meat plants. These have been picked up through the testing and tracing approach that has been adopted, and we are reviewing the guidance.
"We suspect that these outbreaks might have been linked either to canteens or potentially to car-sharing arrangements in those plants.
"And we will be revising guidance to ensure that businesses have the approach that they need to prevent further outbreaks in the future."
During the same session in the Commons, Huddersfield MP Barry Sheerman returned to the topic of meat processing plants.
He asked Mr Eustice: "Does he agree that the future of British agriculture and the British food industry has to be based on quality and shorter supply chains as we come out of this pandemic?
"Will he join me in calling for an investigation into what is happening in our meat processing plants? Some of them look rather strange.
"In the four that I have looked at, many of the workers are reluctant to take a test because they would lose money and be isolated. That is a real problem. Could he look into it?"
Mr Eustice responded: "I agree with the hon. Gentleman that this country has built a proud record based on the quality of our food and food provenance in particular, and we will maintain that.
"On the specific point that he raises about outbreaks of coronavirus at three meat plants, we are looking at that and have been investigating the causes of it. We suspect, as I said earlier, that it is linked either to shared transport or canteen areas, and new guidance will be issued to those meat plants."