I cycled 200 km. My palms are feeling a bit numb and like a mild electric shock is passed through my palms.
Can anyone please suggest any relaxation exercise for my palms?
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I really doubt that you have a palm muscle problem at all. The palm of the human hand has very little muscle (basically just a muscle for the thumb and for the little finger), with no muscles in the middle of the palm. Most of the muscles for your fingers are actually in your forearm.
More likely things:
Getting the bike properly fit to you will help. Improving your core strength with exercises like planks will help. Moving your hands around during a ride will help, which is easier with some handlebars than others. Bigger tires at lower pressure will help reduce the vibration and shock, you may want to consider 28mm instead of 23-25mm tires for longer rides.
Gloves with vibration-damping pads could help, but many gloves cause more pressure on your carpal tunnel or ulnar nerve, so avoid those. Look for a channel or gap in the pads on the palm, and be sure that when your hand is thumb-up the pads won't dig into the bottom side of your hand when in the drops or on the hoods.
Periodically taking one hand off the handlebars entirely can really help a lot with hand issues, and lets you do some hand stretches. If you can't take one hand off the handlebars, you're leaning too heavily on the handlebars and either need to move handlebars up/in or improve your core strength. More hamstring flexibility makes it easier to engage the core muscles to hold yourself up, too.
When you're going over a rough surface, there's a tendency for people to pedal slower, lock up their arms and steer the bike with a death grip. It's better to pedal harder (which shifts weight off your hands and butt), keep a very light grip on the handlebars, and let the bike steer itself straight. Obviously, however, this is only a useful technique for short stretches.
First, there are very few muscles that actually run through the palms. Most of it is either tendons or ligaments, and the tendons are attached to muscles that are in the forearm, not the hand.
Second, what you are describing is a very commonly known (among cyclists, anyway) effect of pressure on the palms which compresses the nerves and blood vessels, resulting in numbness and tingling. The best two cures are to buy a good set of cycling gloves with pads, and shift your hand position often. It's the resting in one spot for a long time that does the most damage.
You could also check your tire compression, too high an air compression will result in more shock from the road being transmitted up through the handlebars.
Also note: Mostly for male cyclists, but to some extent female cyclists, pressure on the perineum (area between the scrotum and the anus) for long periods of time can cause short term numbness/tingling, and if continued for long periods of time (months to years) can cause erectile problems as well. There are bike saddles designed to specifically ease this problem.