I have a gap of 3 years after my M.Sc. Am I eligible for MBA? Will the gap period create any affect later?

There's no constraint of any kind of gap. If you've worked in an organisation, most probably they'll ask for some kind of proof. Or, if you haven't done anything, they'll ask for an application.

As far as I acknowledge, the gap won't be matter if you have utilized those three years at any organisation or at anywhere where you can explain yourself at the interview. Actually, this experience will help you to get more out of MBA rather a fresher can.