Video report by ITV News Correspondent John Ray
During the vegetable harvesting season, the workforce lives in mobile homes based on the farm in Mathon near Malvern and as such they are being treated as an "extended bubble".
In a joint statement, Public Health England Midlands and Herefordshire Council said: "Workers are being asked to remain on the farm during the period of isolation and stay within household groups, to reduce risk of spread within the workforce and into the wider community."
Food and essential supplies are being sent in to the residents while they self-isolate.
A statement on the farms' website said: "We confirm that we are working closely with, Public Health England and the Public Health team at Herefordshire Council to support a number of our workers that have tested positive for Covid-19.
"As a precautionary measure we have arranged for testing of additional key workers including management team members and visitors connected with AS Green and can confirm all results to date outside of our site have been returned with negative results.
"To date there are 73 positive cases on our site.
"Our site is currently closed for all visitors and with the assistance of the various bodies no workers are being permitted to leave our site and are receiving the required support at our site.
"Our work force and local community are our priority at this difficult time and we continue to follow the guidance of the relevant bodies to ensure that the spread of the virus is controlled and our workforce is supported.
"Public Health England advises that it is very unlikely Covid-19 can be transmitted through food or food packaging, so shoppers can remain confident buying British fruit and veg."
According to its website, AS Green and Co is a family-run farm which specialises in growing tenderstem broccoli, broad beans, runner beans and helda beans.