An internal audit of NHS Lothian showed admin staff had been sending drugs to patients due to undergo an endoscopy, without a medically trained member of staff prescribing them.
The audit also showed documents that allow specific patient groups to be given drugs without individual prescriptions had not been completed properly, meaning drugs had been distributed illegally under the Medicines Act.
MSPs and the British Medical Association Scotland have expressed concern.
Dr Brian Keighley, chairman of the BMA in Scotland, said: "There are strict protocols and guidance on who should be prescribing and administering drugs. It is important that prescribing protocols are followed and regulated so that patient safety is maintained."
The NHS Lothian audit team rated the health board "satisfactory" after the probe into prescribing practices and costs, which also revealed hospital doctors may be asking GPs to prescribe drugs not approved by the Scottish Medicines Consortium. However, members of the health board's audit and risk committee said they had "serious concerns" after reading the report and the matter has been handed to Professor Morag Bryce, chair of NHS Lothian's healthcare governance committee.