Sounds like it might be median nerve irritation causing your symptoms (the median nerve does sensation in you thumb, index, middle and half of the ring finger). (PubMed Health / Carpal tunnel syndrome has a good write-up).
As in terms of what to do to improve: it depends on your style of riding. It might help to find a position where you put less pressure on your hands, or use more padding (glove). I used a combination of both to improve my symptoms.

I noticed the same thing on two recent long rides. My right pinky and ring finger were going numb. I mentioned it to my trusted bike shop/fitter. They drove along for one of my rides and observed that my handlebars and position over them, especially if riding in the hoods, needed a tweak. I had a bit too much "locking" of my right arm and elbow. It had been more than a year since my last fit, and I had really increased my bike training volume during that time. Having become lighter, more efficient, and able to ride with a bit more aggressive position, it definitely was cause for me to have the bike fit re-evaluated and "updated."

I would check with your bike fitter to see if they can observe your riding style and position to better assess it.

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The harder you work, the harder it is to surrender.

It helps me to consciously change hand positions every few miles.
Ride in the hoods for a bit, then the drops, then the flats.
If you keep pressure on the median nerve for extended periods of time, it will feel like your fingers are falling asleep.

Have you had a professional bike fit?

Upon returning home from a physically rough deployment to Afghanistan for the last two years I have been having the same problems in both of my hands. Nothing had changed in my bike or equipment so the end theory was that perhaps in some injuries I sustained overseas somehow my overall circulation had been damaged. In attempts to correct it I started with the basics. I got gel gloves with no change. Re-wrapped my bar tapes, nothing. Changed to carbon bars in hope they would smooth out any vibrations that might be the cause, still the same. Received a full and thorough FIT from my local bike shop, hands would still got numb. Tried new seat, upgraded carbon seatpost, tried a different frame and eventually even a new fork all for the same results. Completely defeated until just recently I basically gave up and rarely rode due to the uncomfort. About 2 months ago just for the heck of it I test rode a Specialized Tarmac and to my disbelief my hands did not get numb once! My previous bike had all been aluminum frame and carbon fork. I rode the bike on 2 more rides over the next week with the same results. I sold my bikes and just bought myself a Tarmac 2 weeks ago and I am back in love with ridding! My conclusion is that the carbon frame absorbs enough of the shock and road buzz that my hands don't go numb. I still find it kinda crazy but the results speak for themselves. The only difference right now in on my bike is the frame and fork and somehow it has made my ridding enjoyable. If you are on an aluminum bike I would urge you to try a carbon bike. If you already are on carbon then I am sorry and wish you luck, I defiantly feel for you and hope you figure it out.

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