My job requires travel, which I have had no problems with before. The issue is that I am currently being required to travel to India, specifically an area that was just recently in the news because of aa bombing terrorist attack taking place. It should be noted that I have travelled to this area in India before for work. While this area does not have an official travel alert issued by the U.S. government, I do not feel safe going there anymore due to this terrorist attack and I have voiced my concerns to my Manager.

I fear that I may lose my job over this. Can they legally require me to travel there when I have safety/personal concerns being there?

Yes, they can. If there had been a travel alert issued, that might be different.

Even if there is a travel warning for an area or country, so long as visas haven't been pulled (very rare and in which case i twouldn't be up to your employer whether or not you could travel there) they can send you and terminate you if you refuse. That is not to say they will, only that there is no law preventing them from doing so.