The alarming message was painted in red on a wall in the Russell Road area of the capital, close to Tynecastle stadium.
It reads: "Hang Neil Lennon."
The Northern Irishman was floored by the impact and briefly received treatment, before returning to his feet.
As well as condemning the actions of a few, many fans have also taken to Twitter to condemn the graffiti.
One Twitter user, Dr Mantis Toboggan, wrote: "You don't have to like him, you just have to admit that painting 'hang Neil Lennon' on a wall is unacceptable. Or pelting him with coins. Or people running from the stands to attack him. If you justify that in your head then it's you who's on another planet."
Both clubs have condemned the violence at last night's match which also involved a set of keys being thrown at Hearts goalkeeper Zdenek Zlamal. The goalkeeper also appeared to be assaulted by a Hibs fan at another point in the game.
After the game, Neil Lennon called for a stop to the 'mindless' fan conduct.
Hearts manager Craig Levein called on these 'abhorrent' fans to be banned from football, while the club's owner Anne Budge said the scenes of violence were a 'terrific disappointment.'