Microsoft updates its Authenticator application for Android today, bringing the version number to 6.1.7. The updated app adds fingerprint support, and it doesn't list anything else in the changelog.
There doesn't seem to be an option to actually turn the feature on or off, so it should just work if you've got fingerprint scanning enabled on your device. If nothing else, the feature adds another layer of convenience to two-factor authentication, which can be a bit of a hassle if not using a companion app.
Last month, Microsoft enabled the ability to sign into your account without even having a password for everyone, a feature that was initially added for beta users back in January.
Naturally, the iOS Authenticator app already supports Touch ID, as fingerprint readers are a lot more common on iPhones than on Android devices. You can download the app from the Google Play Store here, where you can also sign up for the beta program if you're into testing out new stuff before everyone else gets it.