Should I state my chronic illness as one of the reason I have few Extra curricular activities in my application for Masters Program?

For US universities, extra-curricular activities are considered important for undergraduate admissions. But this is not the case for graduate admissions - decisions are made primarily based on your academic record, letters of recommendation, research accomplishments if any, and to a lesser extent, GRE scores. Extra-curricular activities are not a factor, unless they are academically related (e.g. engineering clubs and competitions, outside projects, etc). So there's no need to mention those you have done, nor to make excuses for those you haven't.

Clubs and extra-curricular activities can become white elephants on your application, because they are not directly a matter of concern to the admissions unit. By listing those, you run the risk of wasting space that may be gainfully used to highlight more 'curricular' achievements and interests. Additionally, it may give the impression that you are trying to gloss over a lack of academic prowess by mentioning a lot of extra-curricular activities.

In fact, these factors need to be very skillfully woven into your statement of purpose to carry any real weight. For instance, if you experimented with astronomy, robotics and MEMS (considering your mechanical engineering background), but didn't make much progress with any, you could possibly spin that as being open and curious, and trying different things to find your real interest. You could connect these attempts to the way you finally chose the course you are applying for.

As you undoubtedly see by now, extra-curricular activities can be a double-edged sword on your application, so don't bother if you don't have many. I would advise against mentioning your illness as a cause- this may again be misinterpreted.

That said, I would like to point out two types of extra-curricular activities that can be useful, and which some candidates get confused with:

(1) Research projects and internships outside college : For all practical purposes, these are 'curricular'. If you've interned at an industry or research lab, don't shy away from mentioning them (unless they are absolutely unconnected to the rest of your application). Do ensure that you have some evidence of these activities though.

(2) Writing activities: Being in a writing club, editorial board of college/departmental newsletter etc. indicates some proficiency with written English, and this may be particularly useful for a candidate whose first language isn't English.

I agree with the above posters and think furthermore that you should declare a medical problem only with great caution. Even if you're protected by disability laws, you can't control people's negative reaction to anything that's perceived as a flaw. That's a liability in a very competitive admissions process. I would declare a medical condition only if you will require accommodations during your academic program. Even then it's debatable whether a disability should be declared before or after admission to the program. You've already proven that you are capable of doing the work in spite of your condition, so there is no need to disclose it.

Basis of my opinion: editor working with academics with disabilities and on books about coping with chronic medical problems by experts in the field.