US-based research firm Recardio was due to begin a study of the drug dutogliptin on patients in Leeds, Exeter, and Clydebank.
But it has reportedly suspended the UK arm of the trial due to concerns over how new medicines will be approved after Brexit, the BBC reported.
The trial is also running in hospitals in Poland, Austria, Belgium, Bulgaria, Hungary, the Netherlands, Poland and the US.
New drugs intended for use in the EU are evaluated by the European Medicines Agency (EMA), based in London.
The EMA is seeking to relocate to new headquarters in a different EU country after Brexit.
The Golden Jubilee Research Institute, which was informed by Recardio by email on September 17 that one of its research studies had been put on hold in the UK, said the company blamed Brexit.
"According to the company, uncertainty due to EU withdrawal, particularly drug and data release to the EMA, are completely unresolved and represent a significant risk," a spokesman for the institute said.
"However, this may change when the regulatory situation has clarity. Like other NHS boards, we are working closely with the Scottish Government to prepare for Britain's exit from the European Union in order to continue to provide a high-quality service for our patients and staff.
"No patients or staff are affected by the decision by Recardio to put this study on hold.
"Whilst we are disappointed if any clinical trial does not go ahead, we will continue to treat our patients in a safe, effective and person-centred way as well as delivering a wide variety of innovative clinical studies across our specialities to benefit patients across Scotland and beyond."
A Scottish Government spokesman said: "This is the first clinical study we are aware of to be suspended in Scotland as a result of Brexit - and a very concerning sign of what could happen.
"We are working hard to protect Scotland's interests in spite of a lack of clarity and meaningful engagement from the UK Government over our future. With Brexit only six months away, we are doing all we can to plan and mitigate against as many of the significant uncertainties that exist for our health service."
A spokeswoman for the Department of Health said: "We are confident of reaching a deal with the EU that benefits patients and continues to deliver the best possible environment in which to support clinical trials.
"We want to ensure that patients in the UK and across the EU are still able to access the most innovative and effective medicines."
Recardio's founder and president, Dr Roman Schenk, told the BBC that uncertainty over Brexit had created a "very difficult" situation for his company.