IF the tiles have been there a while, and they didn't show any signs of cracking, perhaps the crack in the concrete is just a settling crack.
If the tiles were put in recently, it's hard to tell what the crack may be doing. You could fill it with Concrete Caulk. First, broom some fine sand into the crack to about 1/4" in depth. Then, if you can, pour some water on it to wash it in. If you do this a couple of times and the sand keeps falling down, then who knows how deep the abyss goes. At some point, stop 'watering the sand' and let it dry. Then, after you've put in the last bit of sand to 1/4" in depth (dry), go ahead and caulk with concrete caulk. You may have to 'watch' the crack for a while (IF the tiles are relatively new.) If the tiles have been there a while, again, you should be OK to do something next.
IF you're planning on putting down new tiles, be SURE the caulk is NOT beading up. Otherwise, you won't have a smooth, FLAT surface to do the install. Use your finger to smooth things out or a piece of FLAT plastic, kinda like a scraper. My best to ya and hope this helps.