The striker could face disciplinary action from the Scottish Premiership club after the clip emerged appearing to show the 35-year-old using a derogatory term in reference to Celtic supporters.
The video, which has been widely shared on social media, shows Lafferty reacting when a man posing for a photo with him says “Up the Celts”.
The 85-times capped frontman rejoined Kilmarnock for a second time in January after a spell with Cypriot club Anorthosis Famagusta.
He won three Premiership titles during his time at Ibrox and has also featured for Sunderland, Burnley and Norwich as well as playing spells in Norway, Switzerland, Turkey and Italy.
A club statement read: "Kilmarnock Football Club are aware of a video circulating online which appears to show a member of our playing staff using language of a sectarian nature.
"The club finds all forms of discriminatory behaviour completely unacceptable. The matter will be investigated by the club."