Hello,
I have been working for Amadeus in Bangalore, India as a QA Engineer for the past 1.5 years. I'm here to gather information on MBA programs in Business Analytics.
I have not written GMAT yet and also believe my work experience is less which could limit the colleges I could apply to. I have planned to gather atleast 3 years of experience before applying, but would like to prepare a roadmap.

My current work profile does not include any data analysis. Could that lower my chances?
What universities in US and Europe offer this program?
Should I go for specialized MBA or general MBA with analytics courses?

I suggest you search the discussion board.

It really depends on what you are looking for from such a program. No, you don't necessarily need any data analysis work when applying to the program, but your quant skills as an engineer will come in handy.

A lot of schools have concentrations in business analytics, or at least related curriculum. Since I am more aware of US business schools than European ones, I could suggest that you might start by looking at the MBA programs from these schools:

MIT Sloan
Georgia Tech
Carnegie Mellon (Tepper)
Purdue (Krannert)
Emory (Goizueta)