Can monocycline HCl 100mg one daily make a person tired?

Yes. Fatigue has been reported as a side effect of minocycline, but major tiredness to the point of weakness would be most unusual unless liver or kidney dysfunction was caused by the medication. Of course fatigue could be caused by the illness for which the Minocycline was prescribed.
Yes. Minocycline has some rare but serious side effects. Unusual tiredness is one of them. If this persists , please see your doctor soon.