Mr Hancock said he did not want to impose mandatory jabs for diseases like measles, but did not rule the option out.
His comments came after figures released by Unicef last week showed that more than half a million children in the UK were unvaccinated against measles between 2010 and 2017.
Mr Hancock told The Times: "The evidence is really clear that vaccination is good for you and your children and, critically, protects people who can't be vaccinated for medical reasons.
"Those who have promoted the anti-vaccination myth are morally reprehensible, deeply irresponsible and have blood on their hands."
And he told BBC Radio 4's Today programme: "I do think we need to consider all options. Failure to vaccinate when there isn't a good reason is wrong.
"Those people who campaign against vaccination are campaigning against science. The science is settled.
"I don't want to have to reach the point of compulsory vaccination, but I will rule nothing out.
"I don't want to reach that point and I don't think we are near there, but there is a huge programme of work to increase the proportion of children that are vaccinated.
"If you don't vaccinate your children, it is not only your child that is at risk, it is also other children, including children who for medical reasons can't be vaccinated.
"Vaccination is good for you, good for your child, good for your neighbour and your community."
Earlier this week a Labour MP said the Government should look at making failure to immunise children a "criminal offence".
During a debate in the Commons to mark World Immunisation Week, Paul Sweeney warned the "creeping cynicism" around the safety of vaccinations was a "real national emergency".