Can I just seal a leak in the shower?
As @JimStewart mentioned, in tile showers there is a waterproof "shower pan" usually either rubber, plastic, fiberglass or some other fabric that contains the water that manages its way through the grout joints.  If there is a leak in the pan, any attempt to fix it inside the shower would be futile.

It's hard to see what's going on from the picture, but if you say the water is making its way past the shower curb, you can try to strip all the old calk, re-calk and see if the water still leaks past.  If it does, you may need to tear up some tile for more investigating.