Is our muscle more susceptible to get hurt when its nearer to menstruation period?

Not really: The muscle susceptibilty to damage is not altered by your menstrual period. However, you might feel more muscle pain when you are having your period and a couple days before that. But it's just the sensation that changes, not really the damage it receives.

Small chsnce: Estrogen levels are higher around time of menses & that can possibly cause slight loosening of ligaments which MIGHT make a muscle injury more likely, but overall there is probably not much difference from one time of the month to another