I guess it depends on the noise level, the no. of pixels and the compression used .
I read that for jpeg compression, the compressed file of an image shot with ISO 1600 could be as much as 4 times larger than one shot with ISO 200 because of the high noise level. But then, it didn't specifically mention the camera used and what kind of light conditions.
Out of curiosity, after I've posted, I did an experiment on my camera (Nikon Coolpix 5700) 2 minutes ago using ISO 100 (lowest for my camera) and ISO 800 (highest for my camera). Update now with the results :
1) When shot in jpeg fine quality
a) ISO 100 = 1.8MB
b) ISO 800 = 2MB (an increase of 11%)
The increase is much lesser than I expect. And of course, the file size also depends on the scene.
2) when shot in RAW
File size remains the same at 7.65MB for both ISO 100 and ISO 800. ==> No surprise.