Sir Michael Rawlins, of the Medicines and Healthcare Products Regulatory Agency (MHRA), said supplies of insulin and other medication that is not manufactured in the UK may be disrupted in such a scenario.
Officials need to make sure drugs do not run out if a deal with the European Union is not reached, Sir Michael told the Pharmaceutical Journal.
The Prime Minister has Type 1 diabetes. She has previously said she regularly injects with insulin to manage the condition.
The comments come after new health and social care secretary Matt Hancock revealed officials are considering working with the industry to stockpile drugs, medical devices and supplies in the event of a no-deal.
Speaking in an “personal capacity”, Sir Michael told the Pharmaceutical Journal: “There are problems and the Department for Exiting the EU and the Department of Health and Social Care need to work out how it’s going to work.
“Here’s just one example why – we make no insulin in the UK. We import every drop of it.
“You can’t transport insulin around ordinarily because it must be temperature-controlled.”
Many diabetic people rely on insulin, Sir Michael said, “not least the Prime Minister”.
He said: “Disruption to the supply chain is one of the ways that patients could be seriously disadvantaged.
“It could be a reality if we don’t get our act together.
“We can’t suddenly start manufacturing insulin - it’s got to be sorted, no question.”
Earlier this week, Mr Hancock said it was “responsible” to prepare for a range of outcomes as Britain readies to leave the EU, but insisted he was “confident” a no-deal Brexit could be avoided.
Mrs May later said the public should take “reassurance and comfort” from Government preparations.