The 70-year-old was rushed to A&E after she was struck in the face on Westfield Road outside Sainsbury’s before Hearts’ defeat to Celtic.
The victim is the mother of Hearts’ club administrator Clare Cowan, who told how she had to take her mum to hospital.
She said on Twitter: “To the so-called Hearts fan that thought it was a good idea to throw a full bottle of Bud at a bus of Celtic fans today outside Sainsbury’s car park.
“I’m now sitting in A&E with my 70-year-old mum as that bottle hit her on the side of my face.”
“Shame on you. Your parents must be so proud of the a******* you are.”
Video emerged on Twitter of the moment the woman was injured.
A Hearts fan who witnessed the shocking scenes blasts the thug for hitting a fellow Jambo, saying: “You’re hitting your own.”
The footage, which shows a man running across a street before hurling the bottle, was posted on Twitter by the injured woman’s grandson in a bid to catch the culprit.
He said: “So this is the video of the coward that hit my 70 year old Nana with a bottle before the game on Sunday. If anyone recognises him or knows who he is, please get in touch.”
Police say they are aware of the incident and are conducting enquiries.
A Police Scotland spokesman said: “Police in Edinburgh are aware of information on social media relating to an assault of a woman in the Westfield Road area on Sunday.
“Officers are conducting relevant enquiries to establish the full circumstances surrounding the incident.”
Rival fans continued to clash on the other side of the road, with a video posted on Twitter showing yobs launching objects and confronting each other as they made their way to Murrayfield on Sunday afternoon.
Police said six arrests were made at Murrayfield and praised the majority of fans for their good behaviour throughout the day.
British Transport Police recorded 11 incidents of sectarian abuse and fighting from Celtic, Hearts, Rangers and Aberdeen fans during semi-final “Super Sunday”.
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