Mostly self-sufficient medieval settlement of 1000 humans won't be a city. By this thread it seems that in medieval setting around 90% of people was farmers. This means you have 900 people in villages and only 100 to form a "town" - if you want it self-sufficient. Probably it would be a port settlement, for obvious reasons.
Again, if your setting is medieval, it means you have villages in woods. Typical village had population of 50-300 - so you need about 6 villages and quite a lot of woods between them for it to look like medieval Europe. I recall that one square mile of "used" land can support 150-200 people. This is consistent with already linked source, although I agree it's not truly scientific:
The average population density for a fully-developed medieval country is from 30 per square mile (for countries with lots of rocks, lots of rain, and lots of ice-or a slave-driving Mad King) to a limit of about 120 per square mile
Note that quoted numbers include land that was impractical to use, too.
Let's go with high number. Seems that you need only 5 square miles of usable* land for your population - but you should add quite a lot for things like coastline, patches that can't be cultivated and are inconvenient to build on, woods too hard to cut et cetera.
At 5 square miles, it might look like Hebao Island - as you can see, it's shape makes it impossible, or at least very hard to turn all of it into farms. You need it big enough to have a 5 miles of relatively flat land. how big exactly? Depends on it's geography.
* By usable land, I mean fields, pastures, stables and land for workshops etc. As you can see / calculate, it's about three times more than the estimated field area needed. Some part of this factor comes from less effective methods, some from inclusion of land needed for other uses.