"We are experiencing a rate of infections that we have not seen since the pandemic started," Mr Ramaphosa warned in his weekly newsletter on Monday.
Omicron, detected by South African scientists 10 days ago, "appears to be dominating new infections", he said.
"I call on all South Africans to go out and get vaccinated without delay."
President Ramaphosa, whose country is the worst-hit in Africa for COVID-19, last week hinted at making coronavirus vaccines mandatory.
Despite the rise in infections, fatalities remain relatively low. Just one coronavirus-related death was recorded on Sunday, when 11,125 new infections were diagnosed.
Scientists are keeping a close eye on the new variant to see whether it may be more contagious or virulent, or can side-step existing vaccines.
So far 14.8 million people have been fully vaccinated in South Africa, or around a quarter of the country's population. The rate of vaccination is higher among adults.
With adequate supplies of the Johnson & Johnson and Pfizer shots, the government had initially wanted to vaccinate around 70 per cent of the population by year's end, has moved that target to March 2022.
Seeking to overcome vaccine hesitancy, the authorities at the weekend opened up pop-up sites offering jabs at shopping malls, bus stations, airports, churches and recreation centres.
Private businesses are also helping push the vaccinations numbers up.
Africa's largest telecoms firm MTN said Monday that it will be "implementing a mandatory vaccination policy for staff" starting next month.
"We have a responsibility to ensure that our workplaces are guided by the highest standards of health and safety," MTN president Ralph Mupita said in the statement.
South Africa's largest health insurance company Discovery, which introduced a mandatory vaccination policy in September, said last week that 94 per cent of its staff are now vaccinated.