Danny Yadron and Ian Sherr writing for the Wall Street Journal:

Apple’s new iPhone 5S, which comes with a fingerprint scanner, won’t store actual images of users’ fingerprints on the device[…] Rather, Apple’s new Touch ID system only stores “fingerprint data,” which remains encrypted within the iPhone’s processor, a company representative said Wednesday.

I’m still a bit skeptical and currently don’t plan on using the fingerprint scanner on my iPhone 5s. But, it does appear as though Apple has thought about the privacy concerns and took steps to mitigate them.