Officers stopped the car on the M74 northbound, around 20 miles southeast of the city, around 6.10pm on Saturday.
To their surprise, they found a tiny lamb on the back seat.
The car was searched with the help of a police dog, and Class A drugs potentially worth £10,000 were found.
A Police Scotland spokesperson said: “Officers recovered heroin, with an estimated street value of £7,000 and cocaine, worth an estimated value of £3,000.”
It is unclear how the lamb came to be inside the car - which Road Policing Scotland joked on Twitter was “not a Lamborghini”.
“The lamb has been taken in by a local farmer and enquiries are continuing to establish how the lamb ended up in the car,” it added.
Two men, aged 52 and 53, and a 38-year-old woman were arrested and charged with drugs offences.
They have been reported to the Procurator Fiscal.
