The 52-year-old man was arrested in Khon Kaen province in northeastern Thailand during a routine check by authorities, who found the cubs, aged between six weeks and two months, in plastic crates.
The man was stopped near the border with Laos on Friday after avoiding a police checkpoint.
The driver told police he had been paid 15,000 baht (USD 490) to transport the cubs, media reports said.
Thailand is one of the centres of the illegal trade in tigers. Tiger body parts are prized in many parts of Asia for their reputed medicinal properties.
The driver now faces the possibility of a four-year jail term or a fine of 40,000 baht (USD 1,300) for trafficking of endangered species.
The animals are now in the care of wildlife officials.
More From This Section
Thailand is one of just 13 countries hosting endangered tiger populations.
The global population of tigers in the wild is estimated to number between 3,062 to 3,948, down from around 100,000 at the start of the 20th century.