It comes after Mr Johnson was forced to cancel a trip to India next week because of a surge in Covid cases, thought to be caused by a new variant first identified in the country.
The strain – also known as B.1.617 – was first noted internationally in October and first recorded in the UK on February 22.
It has 13 mutations including two in the virus’ spike protein known as E494Q and L452R.
However, Public Health England (PHE) experts are currently unsure whether any of the mutations mean the variant can be transmitted more easily, is more deadly or can evade the effectiveness of vaccines or natural immunity.
Health Secretary Matt Hancock told the Commons that 103 cases of the variant had been identified in the UK so far.
The quarantine requirements for people returning to the UK from India will come into force at 4am on Friday.
Anyone who is not a UK or Irish resident or a British citizen will be banned from entering the country if they have been in India in the previous 10 days.
Work is being carried out to assess which vaccines will be effective in targeting “variants of concern”, such as the one first found in South Africa.
Health Secretary Matt Hancock said on Monday that 557 cases of the South African variant had been detected since December, with a “cluster” of cases in south London and isolated cases in Barnet, Birmingham and Sandwell over the last week.
While around two-thirds were related to international travel, there has been a “small amount” of community transmission, Mr Hancock said.