Well - it depends what you mean by "diffraction".
Any point along a wave front will act as a point source of wavefronts travelling radially outwards - so while a plane wave will be arriving at the aperture, the waves that come out from the other side will almost look circular.
To me, that's diffraction. Although there will be no regions where extinction occurs in the way that this would happen for wider apertures.
Here is a picture that describes what I'm talking about:
![enter image description here][1]
See also this gif for an animated version
Note that the above holds for an insulating hole. When you have an electromagnetic wave incident on a hole in a conductor, the situation changes as the induced currents in the edge of the hole play a significant role in shaping the transmitted radiation. As shown in the Bethe paper referenced by Ben Crowell, the transmission in that case (for a small, $r\lt\lambda$ circular hole in a perfect conductor) falls off quickly with hole size - it scales with $(r/\lambda)^4$ instead, as you might expect, with $(r/\lambda)^2$.
But your question was about waves on water - so you don't have to worry about the electromagnetic case. [1]: https://i.sstatic.net/pJdQB.png
