People turning up for tests had to be turned away, with the explanation that staff had no hot water to wash their hands.
The site, which is in the South Second Street car park, was re-opened by 1pm and is running as normal today.
A spokesman for Public Health England said: "Severe weather has affected operations at a number of Covid-19 test sites throughout the UK, with several Mobile Testing Units and sites having to close."
He added: "The test site at South Second Street Car Park, Milton Keynes, was one of the sites which had to temporarily close. The site reopened yesterday at 1pm and remains operational.
"Those with PCR appointments who were affected by this closure were redirected to an alternate local testing site. For those unable to attend an alternative testing site, PCR test kits can be ordered for home delivery by visiting https://www.gov.uk/get-coronavirus-test or calling 119."
One member of the public told the Citizen he turned up at the CMK site on Monday morning after booking a PCR test in advance.
"I got there only to be told the pipes had frozen and they have no water. Everyone was being sent home....Why weren't the pipes better insulated?" he said.