Celtic manager Neil Lennon was attacked at Tynecastle during the 3-0 win against Hearts and a man has been arrested for attempted assault following the incident.
During a break in play, a fan clambered from the Hearts section of the main stand and made a beeline for the Celtic boss who was on the touchline, leading to an intervention by police and stewards after the fracas ended and the supporter was taken away by police.
Trouble ensued in the Celtic section of the stadium with fans appearing to fight with police and stewards.
A police spokesman said: "A number of incidents took place during this match including some violent disorder. Lothian and Borders Police will fully investigate all of the incidents that occurred at the match this evening and will work closely with both football clubs and the SPL."
Scottish Football Association chief executive Stewart Regan issued a statement, saying: ''Clearly this kind of behaviour from supporters is wholly unacceptable.
''The safety of players, club officials and match officials is paramount on or around the field of play, and this clear breach of security is a matter I will be discussing with SPL chief executive Neil Doncaster tomorrow.''
Hearts vowed to give their full cooperation to the authorities in a bid to rid the sport of such incidents.
A club statement read: ''An 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 at tonight's match.''
SPL chief executive Neil Doncaster concurred that such acts have no place in the game.
He said in a statement: ''The SPL deplores the actions of the individual involved. This type of behaviour has no place in Scottish football. The SPL will undertake a full investigation and will be reviewing reports from the SPL match delegate, match officials, the police and the clubs.''
Former Northern Ireland boss Lennon has been in the headlines regularly this season for incidents on and off the field. He was involved in a controversy in November over a rejected penalty claim - against Hearts at Tynecastle - for which he later received a touchline ban for his comments.
In January a package addressed to him containing bullets was intercepted at a sorting office in Country Antrim.
In March, the club confirmed Lennon was under 24-hour security surveillance after a suspicious package was intercepted at a Royal Mail sorting office in Saltcoats, Ayrshire.
On April 19 it emerged that Royal Mail intercepted a total of two ''viable'' parcel bombs addressed to Lennon.