Half of motorists in the city were billed for repairs just three years after driving off the forecourt, with brakes, in particular, showing a high fault rate compared to the national average.
Kirkcaldy, in Fife and Lerwick, the capital of the Shetland Isles, were also ranked among the five worst performing towns and cities for MoT test pass rates.
The study found nearly 81% of cars registered in 2010 passed their MoT test last year, the highest pass rate on record. However, in Dundee this fell to 49%, with Kirkcaldy recording a 50% pass rate and Lerwick 53%.
The MoT test data for Dundee shows brakes alone are twice as likely to fail a test compared to the national average.
In Kirkcaldy, drivers were let down by poor suspension, with lamps, reflectors and electrical equipment also problem areas.
Three out of the five worst-performing areas were in Scotland, with Lerwick in fifth place, underlining a north-south divide in car condition. Colder weather, with its impact on road surface, is among the reasons suggested for the difference.
All five of the best-performing towns were in south-east England.
Neil Greig, director of policy for the Institute Of Advanced Motoring, said owners may also be paying the price for skipping routine servicing.
He said: "A well-serviced new car should have no problems passing its first MoT test, so if people are scrimping and saving on servicing in the first three years then that could be a contributory factor.
"There have been suggestions we do not need a three-year MoT test, that we should go for four years instead. But I think as long as we continue to pick up key safety issues such as brakes and suspension then three years is clearly needed.
"However, cars have never been more reliable, so there is something odd going on here.
"There is a possibility the state of our roads, with potholes for instance, are causing suspension problems, but that would not affect the brakes."
Mr Greig added there was "anecdotal evidence" of some mechanics taking advantage of drivers. He said: "A lot of people combine an MoT test with a service, and some garages put the car through its MoT to highlight what needs servicing - as opposed to doing the service and then the MoT test.
"Nonetheless, with a three-year-old car, with a warranty, our advice is you should be getting it serviced annually by the manufacturer or a good garage. That should get you through your first MoT test."
Overall, MoT test pass rates bottomed out at 45% in 1999 and have been rising steadily ever since as motorists began spending more on maintenance or trading up to new cars more often.
However, the study, by motoring website Honest John, reveals popular family car brands, including Renault and Peugeot, are among the worst performers in a first MoT.
For both brands the likeliest cause of failure were issues with lamps, reflectors and suspension, with Renault also scoring poorly for its brake components.
Upmarket brand Chrysler, whose Grand Voyager model costs about £27,000 new, had a pass rate of 55% - making it fifth from bottom.
Daniel Harrison, editor of HonestJohn.co.uk, said: "We have found 20% of all cars fail their first MoT test, but consumers do not necessarily realise their choice of manufacturer and model is an all-important factor in determining whether they pass or fail.
"As our research shows, some manufacturers have the lowest first-time MoT test pass rates but they are still the biggest selling, most popular brands."