This is the result of a misunderstanding (and therefore mistranslation) of the Hebrew (Exodus 34:29):
ויהי ברדת משה מהר סיני ושני לחת העדת ביד משה ברדתו מן ההר ומשה לא ידע כי קרן עור פניו בדברו אתו
The bolded text in Hebrew above, transliterated, says: uMoshé lo yada ki qaran or-panav bedabro itto—meaning ‘and Moses did not know that the skin of his face shone as he spoke with him.’
The word qaran is a verb form of qeren, which can mean either ‘ray’ (of light), or ‘horn’.
Some Latin translations chose—either deliberately, or out of ignorance—to interpret it as ‘horn’, when in fact, what is meant in the original is that his face glowed (presumably as a result of exposure to something during his meeting with God on Mt. Sinai).