There are several commercial products out there for this, but myself, I'd take a page from what a realtor told us to do for a dishwasher once, run "Tang" through it and see if it works.  Possibly even putting it on hold so the water sits in it for a while.

I've since learned that this is due to the citric acid in the Tang, so you could get plain citric acid crystals to use, I'd use whichever is less expensive actually…  Some people have good luck with vinegar too, but I found the Tang the best solution.