Austria can top this, there are towns without street names, so the shortest address you could have for example would be (in this example the number is 0, to not post a real address here) 5222 Ach 0 (Which translates to the town of Ach in the ZIP code 5222, and house number 0) If you write it like this it may be even an international valid address (for some countries) A-5222 Ach 0
Britain is still smaller if we can choose an arbitrary address. S1 1AA There will be hundreds of complete addresses with this pattern, and many thousands if we add a house number before it. This is the first I found that is valid. It's the central post office in Sheffield.
In Austria we also have Buildings that have a 4-digit ZIP code. But it's not a valid address, because a valid address needs a city, street and house number. "5222 Ach 0" has it all ;)