Hearts face serious questions from the Scottish Premier League over how a supporter was able to breach security and reach Celtic manager Neil Lennon in his technical area at Tynecastle.
SPL chief executive Neil Doncaster confirmed an investigation was launched immediately after the incident, which followed Gary Hooper's second-half goal during Celtic's 3-0 win last night.
A fan clambered from the Hearts section of the main stand on to the trackside and charged towards the Celtic boss, who was on the touchline.
A 26-year-old man will appear at Edinburgh Sheriff Court later in connection with the incident, but the SPL investigation will focus on Hearts' security measures.
Doncaster told Sky Sports News: "We'll be focusing on the situation that led to him being able to get access to the perimeter track and that's something we'll be discussing in detail with the home club."
Doncaster added: "The investigation started immediately the incident happened last night. We'll be talking with the SFA and with all the parties involved to investigate it as thoroughly and as speedily as possible."
Any possible sanctions facing Hearts could be influenced by a previous breach of security at their stadium almost exactly two years ago, when Hibernian striker Derek Riordan was confronted by supporters on the pitch.
Doncaster added: "We'll be certainly talking to both clubs, the police and also to our own match delegate, who witnessed the incident, and taking reports from all of those and investigate it thoroughly.
"It's absolutely vital that any lessons that need to be learned are learned and we can put them into effect."
The Scottish Football Association are liaising with their colleagues at Hampden.
SFA chief executive Stewart Regan said in a statement: "In discussions with Neil Doncaster this morning, the Scottish Premier League have confirmed they have initiated an investigation into the unsavoury events at Tynecastle last night.
"I am also aware that Heart of Midlothian are carrying out their own review of internal security measures at the club and have agreed to co-operate fully with both the police and the football authorities.
"I reiterate my condemnation of this blight on the image of Scottish football and expect to see robust plans in place to protect players and officials at all times."
Hearts escaped with a warning after a fan confronted Riordan after he netted a late winner in an Edinburgh derby.
The club later banned two supporters who admitted breach of the peace in court.
The club issued a statement in the wake of last night's incident.
It read: "Heart of Midlothian FC can confirm that a full investigation into events which took place in the second half of tonight's game against Celtic is now under way.
"Hearts is a club which prides itself on its 'Football for All' policy and these sorts of actions have no place in the game of football.
"We will give our full support to the stewards and police authorities in the ensuing investigation into the events."
Doncaster denied Scottish football had a unique problem, referring to incidents "all around the world" and in England this season where fans have got on the pitch, which include a mass invasion following Birmingham's Carling Cup semi-final win over West Ham.
But the former Norwich chief executive admitted this incident was significant because a manager was involved.
And Doncaster bemoaned the fact that the incident overshadowed the continuation of Celtic's SPL title challenge.
Two goals from Hooper and a strike from Kris Commons saw Celtic move one point behind Rangers ahead of Sunday's final fixtures, which see Lennon's side host Motherwell and their Old Firm rivals visit Kilmarnock.
Doncaster said: "That's really the real shame of last night - instead of this morning's headlines being about the exciting climax to the season with just one point between Rangers and Celtic going into the final game this Sunday, and all the traditional passion and drama and excitement and helicopter Sundays that the Scottish Premier League is renowned for around the world, the headlines are about this awful incident.
"I think that's a real shame from everyone associated with Scottish football."