Neither the anemone nor the clown needs a lot of room, so theoretically you would just need enough room for a piece of live rock, the anemone and a little swimming room for the clown. But there are some issues with going too small.
First, anemones should be fed meaty foods. (The clown won't mind either). That means a lot of waste so be prepared to do a lot of water changes -- more so the smaller the tank.
Second, the clown may not take to the anemone. So unless they're already paired, you'll want enough room for the clown to make its home somewhere other than in the anemone's tentacles.
Third, most anemones have a certain amount of light they like and will move around the tank until the find the right light level (and flow). With a small tank, you can keep it in place by depriving it of anywhere to go, but if the light level or flow isn't to its liking, it may not thrive. So you might consider a taller tank, even if the footprint is small.
Fourth, some clownfish can get quite large so you'll want to go with a smaller species like Occelaris or Percula. The problem is these species are known to be more finicky about anemones they'll pair with. You could always try the clown you want and trade it when it gets big. Should be easy to catch in a pico tank.
All that said, if you can maintain reef-quality water, I don't see any reason why this couldn't work with a really small tank or even a cookie jar. I would suggest you consider no sand -- just a piece of rock, the anemone, a heater and a source of water movement -- so you can do a large water change frequently. I think it would be a kind of cool approach to do a pico or cookie jar tank like this and just replace 100% of the water (perhaps sourced from another reef tank) every few days as your primary source of filtration. The live rock should keep the water quality ok between water changes.