The University Hospital in Wishaw has closed a number of wards and a review is taking place into infection levels.
Nicola Sturgeon said the measures in five council areas are 'helping to slow down the increase' in cases.
People living in North and South Lanarkshire will no longer be able to host or visit other households.
Nicola Sturgeon said rising cases in the Lanarkshire region are of 'particular concern' to the government.
Hospital has seen 315 patients receive orthopaedic and plastic surgery outpatient consultations.
A total of 17 employees at the test and trace site in Bellshill have Covid-19 along with seven of their contacts.
The team at University Hospital Monklands in Airdrie said lessons have been learned about the virus.
Staff at University Hospital Wishaw helped an 83-year-old virtually meet his new family member.
