Dr David Rosser, who is the chief executive of the University Hospitals Birmingham NHS Foundation Trust, said that despite stockpiling for Brexit hospitals could face a "completely unprecedented challenge".
The points were raised in a memo to the UHB board of directors last week after being asked to draw up details on readiness for a no-deal Brexit.
Britain is due to leave the European Union on March 29 and MPs voted for Prime Minister Theresa May to return to Brussels to renegotiate parts of the Withdrawal Agreement on Tuesday evening.
In the memo, Dr Rosser said: "In terms of the potential for major operational impact and severe and widespread risks to patient safety, by far the greatest concern is the availability of medicines, devices and clinical supplies."
Dr Rosser said: "It is assumed that a significant proportion of the medicines and consumables we use at UHB on a daily basis may be at risk."
Staffing is another concern raised in the document, with Dr Rosser writing that UHB employs around 1,200 EU staff, of which 262 are doctors and 375 are nurses or midwives.
"It is difficult to prepare detailed predictions or plans for such unpredictable concerns, however it is difficult to see any scenario whereby a no deal or other chaotic Brexit does not significantly impact our ability to safely treat our patients."