Sounds like there is stickiness on my tire, but there isn't!
Ken Hiatt mentioned a wet spot between tire and tube, and I'd like to add something that have already caused me the same symptoms: the anti-puncture band.

In general, there is an overlapping zone of anti-puncture where one tip lays over the other. Depending on how they sit against each other, this might cause this noise. In my experience, this is also a cause of puncture, because the edge of the band can "cut" a groove into the rubber and eventually puncture it.

I wouldn't discard, for the sake of completeness, something inside the rim if it is double-walled (sand, nipple, whatever), or perhaps something related to the loading/unloading of some spoke when the bike rolls with your weight over it.

Hope this helps!