Fix for water damage in tile shower?

to do it properly you really should remove the section that is soft and replace the sub floor and also make sure there is no mold , you can cut a slightly larger then necessary piece and replace without having to replace the whole floor

I would remove it, since it got wet its a mold hazard.

I would remove another row or two of tiles cut the damage out and replace it with cement board then replace the tiles.

What William said is what I'd do . Remove around the damaged area to make sure you got it all . Replace the hardy back , and retile.

I also would do what William suggested, just make sure to go a little beyond the damage so that you know you are attaching new to good board.

I would recommend a professional check it because if that leak is within your wall already it can cause major damage.

sounds like you need a new SHOWER PAN. THis involves a plumber usually or you will end up with the floors around the bathroom getting WET! IT ACTUALLY IS A PAN-SHAPED PLASTIC LIKE SQUARE UNDER THE TILE.

have a professional

(there is an intact pan...the tiles are above the pan.)

Thanks to everyone for your input; since we can't really afford to tear it all out and do it right, will go a few rows beyond the damage to be safe(r). We have cement board, and will use it as a base.