Defining what a city is, is a wee bit more complex than measuring its length. But to answer your question, the worlds smallest city that has record of its size is Hum, Croatia and its only a little more than 4 sq km so it reasonably could be as little as 1/4 mile long, and it has a population of 20 as of the 2011 census.

Vatican City is a bit more than half a mile long and just under 1/2 square miles area.