The board would not divulge the circumstances behind the cases but confirmed on Monday that the four patients involved were not in any of the board’s three acute hospitals -and were self-isolating at home with relatives.
However, another new case was confirmed within the board area on Tuesday morning.
The rest of the cases -totalling four- are in the Greater Glasgow and Clyde area.
Karen McGuigan, NHS Lanarkshire consultant in public health revealed: "NHS Lanarkshire's Test and Protect team is in the process of identifying all close contacts of the cases who are being given public health advice and being told to get a PCR test and self-isolate.
"We are working closely with the Scottish Government and Public Health Scotland to ensure that all control measures are in place to reduce risk
"Take a lateral flow test before you socialise to reduce the spread of the virus. Self-isolate and take a PCR test if you have symptoms, wear a face covering, keep washing your hands and get your vaccine and booster.
"To respect and maintain confidentiality for the patients involved, it is not possible to release any further information at this time."
For more, see page 4.