To less experienced eyes, the Lilliputian vehicle might have seemed an unlikely prospect for auction stardom. After all, the ancient Austin Mini lacked doors, side windows or even a radio. It sat on tiny 10-inch wheels, offered occupants only hard wicker seats and was powered by a petite, motorcycle-size engine.

But Mary Falvey, whose father was a prominent Michigan dealer and distributor of European cars, knew better. The Mini had been in her family since it was built 57 years earlier. Part of a British Motor Company promotion to increase Americans’ interest in small cars, the vehicle — still in original condition — was one of only 14 made.

“It had charm, rarity and a role in automotive history,” she said.

Ms. Falvey might have offered the vehicle through a traditional auction house or, perhaps, at an established storefront dealer. Instead, she listed the Mini online with Bring a Trailer, a fast-growing website that now counts two million monthly visitors and 100,000 registered bidders.