The checks were triggered after controlled drugs were found to be missing from the ship’s medical station.
Stena said it had a zero alcohol policy for staff but refused to confirm a report that up to 20 workers were tested and about five suspended in the incident last month.
Its spokeswoman said: “Stena Line can confirm that as a result of random testing, a number of employees onboard its Belfast–Cairnryan operation have failed the test and as a result Stena Line is now carrying out a full investigation as part of its established disciplinary process.
“We can confirm that it was identified through routine inspections onboard that controlled drugs were missing from the ships medical station that is in a secure location onboard the vessel. For this reason we carried out a drug and alcohol testing.
“The police were notified immediately.”
Belfast Harbour Police confirmed it had been called in.
Its spokesman said: “The matter has been referred to Belfast Harbour Police and remains under investigation.”