Britain last week re-imposed a 14-day quarantine period on people arriving from Spain.
Matt Hancock says a second wave is starting to "roll across Europe".
"So, absolutely, on a second wave it is something I worry about and I worry about it because we can see it happening", he added.
Speaking to Sky News, he said: "I am anxious about a second wave".
The warning comes as people who test positive for coronavirus or display symptoms must now self-isolate for 10 days as Health Secretary Matt Hancock warned of a "second wave starting to roll across Europe".
No indication new coronavirus is seasonal
In temperate areas of the northern hemisphere, influenza activity has "returned to inter-seasonal levels". Referencing heightened case numbers during the summer in the U.S.
Hancock said the government is working on using testing to cut the 14-day quarantine period for those returning from countries which have seen spikes in cases of the virus, but ruled out any imminent change to the rules.
"The measures that the chief medical officer will set out later are part of that, but so too are the measures we're taking, for instance, to ensure that we don't directly bring cases back to this country where there's a big spike in cases".
Hinting that these changes could go ahead, Hancock said: "This is a decision that's clinically led". That is why we had to take the action that we did. But we can only continue to grow with your support.
He said the best way to keep the virus under control was if we had "tough swift and decisive lockdowns" in order to protect the whole of the UK.
He said the virus was "bubbling up a little bit" in 10 to 30 places within the United Kingdom, and that it was vital Britons stuck to social distancing rules, washed their hands, and got tested if they had any symptoms. "And we are absolutely determined to do everything that we can to keep this country safe", he said.
Mitt Romney proposes compromise on logjammed pandemic aid
It would provide another round of $1,200 direct payments based on the same formula from the earlier aid bill. Susan Collins, R-Maine, cosponsored the legislation with Romney, and said it is a reasonable compromise.
He said: "This is a really important, essentially scientific question, but we are not imminently making an announcement on it".
He said: "We are always looking at ways in which we can mitigate the impact of the quarantine, try to help people, try to make sure that the science is working to help travellers and holidaymakers".
People who test positive for the novel coronavirus or show symptoms in the United Kingdom must now self-isolate for at least 10 days, rather than seven, it was announced by the country's chief medical officers on Thursday.
Wales has announced an increase in the time you need to self isolate if you have symptoms or a positive test result.
"We can no longer hide from the fact the Government has not handled this crisis well and needs to urgently learn lessons from its mistakes", he added.
Tulsa's Black Lives Matter message to be erased
NSW Premier Gladys Berejiklian had earlier on Tuesday appealed to "people's conscience and ethical standards" not to attend. The giant letters spelling out Black Lives Matter were painted overnight right before Juneteenth and the Trump rally.