Sajid Javid told MPs that Omicron cases could reach 1 million by the end of the month.
The health secretary told the House of Commons that there are 568 confirmed cases of the Omicron variant, but that the current number is probably closer to 10,000.
The UK health security agency estimates that the number of infections is 20 times higher than the number of confirmed cases, so the current number of infections is probably closer to 10,000.
By the end of this month, the UKHSA believes that infections could exceed 1 million, due to the observed doubling rate of between two and a half and three days.
Javid said that there was a lot to learn about the new variant, but that there was now confidence that Omicron is far more transmissible than Delta.
He said that the cases of Delta had doubled in a few days. Omicron was spreading at an even faster rate.
It has been around for between 2.5 and three days based on the latest data.
Scientific advice to ministers on Tuesday gave a stark outline of the consequences of failing to take action to suppress the spread of the virus.
The advisory committee of the Scientific Pandemic Influenza Group on Modelling predicted on Tuesday that there is a chance of a large peak of infections in the UK if initial estimates of transmission advantage and immune escape from South Africa are applicable to the UK population.
The scientists said that even if the severity were half of Delta, this could still be more than enough.
The scientists said it is likely that strict measures would be required to control growth and keep R below 1 if Omicron has some transmission advantage.
Omicron is on a steep upward trajectory in the UK, with thousands of daily infections already occurring and a projection for Omicron to become the dominant variant within a few weeks.
Without any changes to measures in place, the number of hospital admissions from Omicron could go up to 1,000 per day or more in England by the end of the year, with a peak likely to be higher than 1,000 to 2,000 Omicron hospital admissions per day.
The minutes said that for it to be below this level, there would need to be a small degree of immune escape and high protection from boosters.
The advice released by theSage suggested that hospitals, care homes, and prisons should consider additional infection control measures to help prevent the spread of the highly transmissible variant.