A supporter in the away end was filmed breaking a seat before throwing it further forward in the stand.
The footage was accompanied by a tweet which read: "This p***k about 6 rows in front spent half the game singing Fathers Advice and the rest giving Red Hand salutes, ripped up three seats at full time before chucking them and hitting his own fans. Get these p***ks out of our club. Hearts vs Hibs, Easter Road, April 28th 2019."
The post was noticed by Dempster who shared it on her timeline, saying she will contact Hearts to try and identify the fan and have him banned from Easter Road.
She noted that the damage will cost Hearts £60.
Dempster tweeted: "You just cost your Club around £60 mate - this will be shared with our colleagues at @JamTarts to see if we can identify you and have you banned from OUR stadium in the future. We are all sick of this type of behaviour. #callingyouanidiot."
It is not the first time this season that a controversial incident has happened off the field in the derby. There has been incidents of coin throwing, players being assaulted, racist abuse and flares or smoke bombs thrown onto the pitch.
Sunday's game finished 1-1 with Uche Ikpeazu's late strike cancelling out Christophe Berra's own goal. Hibs' Marc McNulty had missed a penalty prior to Hibs taking the lead.