Answer:
Vatican city is the smallest sovereign country in the world, with an area of 0.44km². This is so small, in fact, that it actually has 2 popes per square kilometer. Tiny countries like this are called city states. They are always a bit problematic when comparing countries with each other because city states are always way denser and richer than 'real' countries.
For example, if you compare countries on GDP (PPP) per land area, number one is Monaco with a mind-bogglingly $3.1 billion/km². By comparison, the highest 'real' countries are Quatar, the Netherlands and South-Korea with $17 million/km².[1]
So what is the smallest 'real' country? There is no official definition, but if I had to make one I would say it should have at least 3 cities and not be part of another countries territory (like Bermuda or Aruba). In which case I nominate Luxembourg, at a comfortable 2,586 km²