Hearts defender Clevid Dikamona told an abusive Hibernian fan that he could not take away his derby victory joy after being subjected to abuse at Easter Road.
A fan was seen on live television shouting apparent racist abuse as the French-born Congo international was being told to leave the pitch by the referee following treatment for an injury during Hearts' 1-0 Ladbrokes Premiership win.
Hibs vowed to identify and take action against the individual and Dikamona responded to footage of the incident on Twitter.
The 28-year-old wrote: "You can't know how happy and grateful I am tonight, despite what he could do or say he will not take away that feeling, I prefer to smile and tell you that I love you."
A Hibernian spokesman said: "The club will do everything we can to identify the individual concerned and we will take the appropriate action. It's unacceptable."
Campaign group Show Racism the Red Card Scotland condemned the Hibs supporter and called for action to be taken.
A statement on its Twitter account read: "After the racist abuse captured on tv today. We will be writing to @HibernianFC demanding action is take against the perpetrator. Racism has no place in Scottish football."
Hibs midfielder Marvin Bartley expressed his sorrow after watching the footage.
Bartley, who was on the bench for his team after recovering from injury, wrote on Twitter: "Result aside, believe me I'm just as hurt by today as you are but seeing one of your own 'fans' say this is truly heartbreaking!"
The previous Edinburgh derby at Tynecastle saw Hibs head coach Neil Lennon struck by a coin and other missiles thrown at Hibs players and match officials, while a man was later charged in connection with an alleged assault on Hearts goalkeeper Zdenek Zlamal.