Sajid Javid said the UK Health Security Agency had detected cases in Chelmsford, Essex, and in Nottingham.
He said the cases were linked and the two people were self-isolating alongside their households while more tests and contact tracing take place.
Ten countries are now on the UK's travel red list meaning, from Sunday at 04:00 GMT, all arrivals will have to quarantine in a hotel for 10 days.
On Friday, the UK placed South Africa, Namibia, Zimbabwe, Botswana, Lesotho and Eswatini on the list.
sked about potential changes in Covid restrictions, Mr Javid said: "We will do whatever is necessary to protect the progress we have made as a country. We've come a long way since the summer and we keep all of this under review and if we need to take further action, we will."