Hand cream, lotion? Wash hands for some time under warm water? If it is dry hands, that should help.
Keep in mind, that TouchID is now associated with safety enclave (or whatever) and that failure in that system really can cause issues... So, do you have backup? Current? Checked? Just in case that system is failing...
Reboot may help, that will power system down and up. Log out/log in does not power cycle the system... Before you do that - do you have backup?
I have external keyboard with touch id - if you have chance to use that one, does that touch id work?
Could be hardware failed, in which case Apple store Genius bar should be able to verify and provide estimate for repair.