Celtic chief executive Peter Lawwell has called for Scottish society to address the "fundamental issues" which he feels are behind "vile, sustained and relentless attacks" against his club and manager Neil Lennon.
Lennon was the subject of an alleged assault at Tynecastle on Wednesday night and a package containing ammunition was found at Celtic Park on Thursday.
In a statement, Lawwell said the Tynecastle incident "brings shame on Scottish football and again highlights the fact that Scottish society must address fundamental and serious issues which lead to outrages of this kind".
He added: "It is intolerable that any football club, or individual, going about their lawful business in the name of sport should be subjected to this ongoing campaign of hatred and intimidation. This is Scotland's shame and it is high time Scotland addressed it.
"Since moving here a decade ago, Neil Lennon has had to endure prejudice and violence both as a player and manager, having suffered no such problems elsewhere.
"In doing so, he has displayed a strength of character and resilience which deserve respect from all who oppose the campaign of intimidation against him.
"He is a man who is proud to be the Celtic manager and is someone who simply wants to be able to carry out his role in the same way as every other football manager can.
"Clearly, Neil will continue to receive every support and protection from Celtic Football Club."
Lennon has had round-the-clock security since March 4, when the first of two parcel bombs addressed to him was intercepted at a Royal Mail sorting office. Two men were arrested today in Ayrshire in connection with that police inquiry.
The package found at Celtic Park on Thursday contained a bullet and is believed to have been addressed to Lennon - the second time such an item has been sent to the former Northern Ireland international this year.
A man later appeared in court charged in connection with the Tynecastle incident, which took place after Gary Hooper scored the second goal in Celtic's 3-0 victory.
John Wilson, 26, of Edinburgh, was charged with breach of the peace aggravated by religious prejudice and assault aggravated by religious prejudice. He made no plea and was remanded in custody. Hearts later handed Wilson a lifetime ban.
A club spokesperson said: "While not wanting to prejudge the outcome of the court case, all true Hearts fans will have been disgusted by what they witnessed last night.
"There is no justification for such actions, which have no place in the game of football, and we have taken the severest action open to set the strongest possible deterrent.''