Audi A1 buyers may have to join a waiting list, as demand looks likely to exceed the 50,000 cars being built this year.
"In view of the high demand, orders could surpass the production capacity this year," Peter Schwarzenbauer, Audi's head of sales and marketing, told Automotive News Europe.
The Audi A1 will cost from £13,145 in the UK.
Audi estimates 90 per cent of interested buyers are first-time Audi customers, and is particularly keen to use the A1 to attract them as affluent young buyers traditionally move on to mlarger models in a make's range as they grow older.
Audi will ramp production up to 80,000 cars in 2011 and 100,000 cars beyond that.
Production of the Audi A1 began yesterday (Tuesday), with 500 cars being built a day.