ibra,
It could be from a few different things, some benign, some serious.
Occasionally, when we walk, and swing our hands, fluid can build up in them. If you have a subclinical carpal tunnel syndrome, the extra swelling for the fluid, can put pressure on the nerve, causing the fingers/hand to go to sleep.
However, it is also possible that you have a stenosis in one of the arteries to the left upper extremity. Then when you walk, not enough blood gets to the extremity, causing ischemia to the nerves, causing numbness.
However, the only way to know for sure is to be examined by your physician. If it continues or is associated with pain, you might want to see someone about it.