The melee in front of the dugouts at Tynecastle following the alleged attack on Celtic manager Neil Lennon.
The male officer was assaulted as police tried to control the away support in the wake of the incident, which saw Lennon apparently attacked by a fan who had invaded the pitch.
It is understood police were unable to make an arrest at the time because of the sheer number of people involved in the surge, but they are investigating the incident.
It comes as concern has also been raised after several Facebook sites were launched - attracting thousands of "likes" - in the wake of the Wednesday night incident.
Hundreds of bigoted comments were made, by those claiming to be both Hearts and Rangers fans, about Lennon, a Northern Irish Catholic who has been subjected to more than a decade of sectarian abuse.
One user wrote "die die die, Lennon, Lennon die", while the administrator of the page - who concealed his own name - observed: "Neil Lennon's gonna end up like his brother John if he doesn't get some security guards".
The incident that flashed across television screens all over the world has brought the sectarian issue straight on to Edinburgh's doorstep.
Lennon was today reported to have told friends he is "not safe anywhere". The 39-year-old manager has received parcel bombs, bullets in the post and death threats, and even had a panic button installed in his home, but the focus of those inquiries had been in Northern Ireland and the west coast.
But now Hearts fans - whose rivalry with Celtic is deemed almost as ferocious as Rangers' - have been dragged into the ongoing row.
Supporters on Facebook proudly declared that the stadium was "jumping" after the flashpoint, while another fan added: "Next time he comes to Tynie let's let him know just how much he is hated. Let's pitch invade and pillage."
Fans of Rangers also weighed in with their support.
One said, "That was the third best moment of my life", while another online comment stated, "Just a pity there wasn't another 20 of his mates following him. That guy deserves a medal."
No sooner had the tribute pages been set up than rival sites appeared, calling for justice to be done. The incident capped what was already a tense night for fans.
A spokesman for Hearts said: "Hearts worked with Celtic, the police and stewards weeks in advance of the game to ensure all provisions were made to ensure the safety and security of staff and visitors to the stadium.
"As a result the game was flagged in the highest possible category and police and stewarding levels were increased accordingly. However, the intent and actions of one individual to breach security measures put in place has tarnished the club and the wider game in this country as a whole."
John Clark Wilson, 26, of Edinburgh, was yesterday given a life ban from Hearts and appeared in private in court, charged with breach of the peace and assault, both aggravated by religious prejudice. He made no plea or declaration and was remanded in custody.
As a lifelong Hearts supporter I always took great pride in hearing football players and managers lauding Tynecastle as a great stadium to play in as the atmosphere was always "a bit special". Sadly, I fear that view may have changed forever following the incidents at the Celtic game on Wednesday night.
On taking my seat in the Wheatfield stand I noticed that the Celtic fans were in an exuberant mood (surprising given that they were four points behind Rangers) and it looked like the whole away end were on their feet shouting and singing. Hearts fans, happy in the knowledge that we had secured third place, were responding but were finding it difficult to compete with the repertoire of songs emanating from the Celtic end.
Unfortunately, part of the repertoire included not just the familiar rebel songs but more up-to-date references to the IRA and the Queen, inviting a response from some fans with the "Gorgie Boys", containing the line "we are up to our knees in fenian blood, surrender or you'll die", both equally worrying in their content and totally out of place anywhere. But we had heard this before, so what was different?
There is no doubt in my mind that many spectators were charged up by seeing the man they love to hate, Neil Lennon. Not helped by recent statements attributed to him, there was an air of aggression not normally present. With Celtic one-nil ahead, David Obua was inexplicably sent off and the blue torch paper was now alight.
In the second half there was a security breach and Neil Lennon was attacked, which sparked off unrest at the Celtic end with a huge brawl ensuing between supporters, police and stewards.
The vast majority of Hearts fans are proud of their team and its history and I have no doubt would be abhorred at what they witnessed, particularly parents with children. This was not the norm and cannot be condoned.
To ensure this does not happen again, however, we must enlist the help of all interested parties to put the lessons learned to good use.
Edinburgh is a fantastic city with warm, welcoming people. We cannot allow this behaviour to tarnish our reputation at home and abroad.
I will be renewing my ticket for next season and cheering on the team.
And I will do everything I can to ensure that we do not witness such scenes again. We can all play a part in this. It is, after all, only a game of football.
Other parts of the world have more pressing, life-threatening matters to deal with – surely we can sort this out.
Councillor Steve Cardownie is deputy leader of Edinburgh City Council