Britain last week re-imposed a 14-day quarantine period on people arriving from Spain. Some other European countries which are currently exempt from the British quarantine measures have seen infections rise, Hancock said, without naming them.
"I am worried about a second wave. I think you can see a second wave starting to roll across Europe, and we've got to do everything we can to prevent it from reaching these shores, and to tackle it," Hancock said during an interview on Sky News.
"We have significant concerns about the second wave that is coming across Europe. And it's not just Spain ... but there are other countries too where the number of cases is rising. And we are absolutely determined to do everything that we can to keep this country safe," he said.
Hancock said the authorities were working on possible ways to shorten the quarantine period for people coming from Spain but no change was imminent.
"We are working on whether by testing people during that quarantine it is safe to then be able to release them earlier ... But we are not imminently making an announcement on it," he said in a BBC television interview.
"That work is not concluded. Until it is absolutely safe to make that sort of change then we won't do so ... We won't be making changes on that in the next few days."