Celtic and all the other SPL clubs will wear poppies next weekend
Celtic aim to ban those found responsible for a giant anti-poppy banner displayed at the weekend.
The protest unveiled on Saturday read: "Your deeds would shame all the devils in Hell. Ireland, Iraq, Afghanistan. No bloodstained poppy on our Hoops."
Celtic issued an apology for any offence caused and will launch an investigation aimed at banning the perpetrators from home games.
All 12 SPL clubs will wear poppies on their shirts next weekend.
Scottish Premier League chief executive Neil Doncaster confirmed that the governing body would also investigate the matter.
These incidents do need to be investigated and they are going to be
Scottish Premier League chief executive Neil Doncaster
"It's clearly regrettable that a weekend of so much excitement on the pitch has been dominated by reporting of events off the pitch," said Doncaster in relation to the banner at Celtic Park and crowd trouble during the Edinburgh derby.
"We have invited comments from Celtic, Hibernian and Hearts on the back of the weekend's events and are awaiting the reports of the match delegates."
A section of Celtic fans have long campaigned against the wearing of poppies.
But Doncaster said it was now an established practice in the SPL for all clubs to wear poppies on their shirts on the weekend of Remembrance Sunday.
"We would welcome the fact that Celtic have moved quickly to apologise," he said.
"I would also point out that all 12 of the SPL clubs will be wearing poppies on their shirts next weekend in support of Poppy Scotland for the third year in a row."
Doncaster would not be drawn over whether the banner was a breach of stadium rules forbidding political demonstrations but added: "There have been a number of instances of inappropriate behaviour at games.
"These incidents do need to be investigated and they are going to be."
Celtic responded to the controversy by issuing a statement which said: "The actions of this small minority have no place at Celtic Park and, clearly, we apologise for any offence caused."
A spokesman later added: "The club is currently carrying out an investigation into this matter. When it is concluded, it is the club's intention to ban those identified as responsible from Celtic Park.
"Celtic fans have rightly earned a magnificent reputation for their positive behaviour and backing of the club.
"It is extremely disappointing that the actions of a small minority have embarrassed Celtic and tarnished the club in this way."
The charity Poppy Scotland described the banner, displayed during the 9-0 win over Aberdeen, as "disrespectful".
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