Using an untrusted computer to log into secured accounts always carries an element of risk, as the environment may be compromised. However, the firmware on the YubiKey as well as the Security Key by Yubico prevents the secrets and keys stored within from ever being extracted from the device; this means that malware is not able to steal the credentials that would be needed to duplicate your YubiKey. That said, if you sign into a website on a computer with a compromised OS, browser or application, it could potentially use that login session to perform unauthorized actions on your behalf.
You should avoid using untrusted computers to log in to your accounts, but if you must use one be sure you log out after you are done so the login session is no longer valid.