Though voluntary, the new licence, which takes about two hours to obtain and costs €25 ($30), has both written and practical "driving" tests to assess the owner's competence.
For the written part of the exam, candidates must answer multiple-choice questions that check whether they know their responsibilities concerning their pet's health and behaviour.
"When your dog wags its tail, does it mean it is happy, excited or bored?" is a typical question.
The practical part simulates a drive - in this case a "walk" - through town, testing the owner in a variety of predicaments such as putting a muzzle on the dog in the tram or underground, or picking up droppings.
Ulli Sima, the capital's environment councillor who initiated the licence project, said: "The Viennese are real dog-lovers. But they believe strict measures are necessary so that peaceful cohabitation between man and dog is possible in this city."
Those happy owners who pass their "licence" - or Hundefuehrerschein - will be exempt from the annual dog tax of €43.60 and will receive a few goodies for their pets, from vouchers for a new leash to bags for their pet's droppings.
The initiative was triggered by a survey of 500 Viennese residents in September 2004 in which a surprising 85% backed the idea of instituting a "driving licence for dogs".
Vienna officially counts about 47,000 canines - meaning those subject to a city dog tax - but estimates say there could be up to 150,000 hounds for a population of 1.7 million humans.
Karl Woegerer, Vienna's deputy environment councillor, said: "This is not about pure obedience, but rather about social tolerance of the dog-owner team in the city."
He said the Viennese initiative "is unique in this form, although licences exist in several German states".
A licence, following a test, is already required for guard dogs for security reasons, a measure in place in many countries. The new licence is for the average street pooch, which many still find intimidating.
In the 2004 survey, 34% of those questioned said they felt "personally in danger" in the presence of dogs, and 92% said dogs should always be kept on a leash and wear a muzzle.
According to the Vienna-based non-profit organisation Animals as Therapy (TAT), at least 15 people are known to have passed the test, but official figures are yet to be released.
Elisabeth Karsai, a medical student associated with TAT who took the test with her two-year-old grey poodle, said she "felt like a pioneer and wanted to ensure that more people pass this licence".
According to Gabi Glaser, TAT director, the point of the test is to know the basic rules of how to lead a dog and to make life with canines as pleasant as possible in a city.
"Dogs' social tolerance and ability to deal with a big city will be improved and in this way people's safety needs will also be satisfied," Sima was quoted as saying on the city's website.