Speaking to ITV News, Mr Hancock pointed to Chancellor Rishi Sunak and Home Secretary Priti Patel as being from ethnic minority backgrounds.
Pressed on there being no black members in the current line-up, Mr Hancock said, "there were until a couple of months ago".
"The most important thing is that we have that diversity throughout the government and the key thing is taking action to ensure that people have equality of opportunity," he argued.
In the current cabinet of 22, there are no black or LGBT members and only six women.
Thousands of people are attending Black Lives Matter (BLM) rallies across the UK in the wake of the death of George Floyd, a black man who died in police custody in Minneapolis.
Mr Hancock said he "sympathised enormously with the cause" but called on people to "make the argument safely".
"I think driving for true equality of opportunity across this country is incredibly importantly," he told ITV News.
"I do want people to put that argument and I will support people who make that argument.
"But the challenge is we are still living in the middle of a pandemic and we're still trying to get the number of infections down.
"But it's a biological fact that gathering in large numbers without social distancing risks the increased spread of the virus and that risks lives.
"I urge people to make the case and make the argument but follow the social distancing rules and follow the law because that's the best way to make the case in a way that keeps people safe."
Mr Hancock also defended the easing of lockdown restrictions despite the R number (the rate of transmission of Covid-19) rising in parts of England.
He went on to avoid answering a "hypothetical question" about how localities could be locked down if rates of the respiratory disease were rising but people had to travel to or from the area for work.
Mr Hancock said he could not answer whether someone who lived in an unaffected area but worked in a place that had been put on lockdown as it was "not based on something that's happening right now".
"I'm not going to get into hypothetical questions, I'm going to talk about what the policy is," Mr Hancock said.
In the north west, the R value - which indicates how fast a disease spreads through a population - is close one.
Manchester mayor Andy Burnham has criticised the government, saying it has loosened lockdown too early and linking it to the rise in the Covid-19 R number in the region.
The health secretary said regional lockdowns would be imposed in areas - or within hospitals and care homes - where there was an outbreak.
But Andy Burnham and his Liverpool counterpart Steve Rotheram said they had not been consulted and told ITV News they do not know how the plans will work.
Mr Rotheram accused the government of not having the details he is asking for on local lockdowns, calling them "back of a fag packet" plans.