Mildew Smell in Ice and Water from Refrigerator?

If there is some way to get to the lines, run a mild bleach solution through them to kill the mildew, then flush with clear water until no more bleach smell.

My fridge has a filter. I would try changing that and then run a gallon or so of water thru, then throw out all old ice and start over, and see if that helps.
Take make & model number of fridge with you when you go shopping, as filters are not all the same size.