Scientists believe that the variant is more transmissible and cases of it nearly tripled to 1,313 in the past week in England.
But Matt Hancock said early lab data showed vaccines remained effective.
He said the majority of those in hospital in Bolton – a hotspot for the Indian variant – were unvaccinated.
The health secretary said that the variant, known as B.1.617.2, was “relatively widespread in small numbers” in most of the country.
It comes as England is due to move to stage three of the government’s roadmap for easing lockdown on Monday, with socialising in groups of six indoors as well as some international travel to be allowed.
On Friday Prime Minister Boris Johnson warned the variant could pose “serious disruption” to the final stage of lockdown easing in England on 21 June.