New restrictions: Bars and restaurants will not be able to serve alcohol, remote working will be compulsory where possible, mask mandates will be extended and access to public swimming pools and gyms restricted.
Cancelling large sporting events was also recommended. The measures will come into force overnight from Tuesday to Wednesday and are due to last four weeks.
South Africa first reported Omicron to the World Health Organization last month. Early data suggest the variant is more transmissible and resists vaccines, prompting several countries to reimpose restrictions and travel bans.
Norway, a northern European nation of 5.4 million people, has recorded 317,870 Covid-19 cases and 1,136 deaths since the start of the pandemic.