He told the Health Select Committee that he had met with medical industry leaders to "accelerate" preparations for the possible outcome in March next year.
Hancock, who was appointed health secretary two weeks ago, said he was confident the UK would reach a deal in negotiations but said it was "responsible" to prepare for all outcomes.
"We are working right across government to ensure that the health sector and the industry are prepared and that people's health will be safeguarded in the event of a no-deal Brexit," he told MPs on Tuesday.
"This includes the chain of medical supplies, vaccines, medical devices, clinical consumables, and blood products.
"And I have asked the department to work up options for stockpiling by industry."
The NHS depends upon the free, unchecked flow of vital medicines and supplies from elsewhere in Europe and failure to secure a deal before Brexit would likely cause significant disruption to treatment.
The UK relies on 370 million packs of medicine from the EU a month, as well as blood plasma supplies and radioactive isotopes used in X-rays.
Simon Stevens, chief executive of NHS England, said earlier this month that "significant planning" was underway to prepare for all outcomes.
Labour's shadow health secretary Justin Madders said the preparations represented "the terrifying reality of this government's failure to prioritise the NHS in the Brexit negotiations."
"We need a Brexit deal which puts patients first but now we know that the NHS is having to stockpile medicines because of this government's chaotic handling of Brexit," he said in a statement.
The prime minister would also struggle to push through a much softer or harder form of Brexit through parliament, however, leading some to believe that a no-deal scenario has become a highly realistic one.
If Britain fails to reach a deal by March next year, it will automatically leave the EU.
That is why May has told government departments to "accelerate" no-deal planning. They plan to issue weekly guidance to busineses and households over the summer on how to plan for a no-deal Brexit.
Brexit secretary Dominic Raab also told MPs on Tuesday that the government would take steps to ensure there was an "adequate food supply" if the UK leaves without a deal next year.
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