Celtic have temporarily banned 128 fans and have announced they are to break up the Green Brigade section at Parkhead.
In a statement, the club announced the action following the behaviour of fans during Friday night's Scottish Premiership away match at Motherwell, during which seats were ripped out and smoke bombs were thrown onto the playing surface.
After the SPFL condemned the "shameful scenes", Celtic have now moved to take action against those they deem responsible.
A total of 250 season ticket holders located in Section 111, where the Green Brigade are located at Celtic Park, will be moved elsewhere inside the stadium.
In addition, 128 fans have been banned pending investigation by the club and won't be permitted to attend Celtic matches either at home or away.
A statement from the club read: "Following events on Friday evening at Fir Park Stadium, Celtic Football Club today announced that it has issued precautionary suspensions against 128 individuals preventing them attending matches involving Celtic, pending further investigation. These suspensions will cover matches at Celtic Park and away matches.
"In addition, the club will be relocating around 250 season book holders in Section 111 to other areas within the stadium, or offering refunds covering the remainder of the season to those who do not wish to be relocated.
"Events such as those on Friday night do not represent the Celtic support or the club. These events were an embarrassment to our great football club and are absolutely indefensible.
"It is clear that there is an element which has no hesitation in bringing Celtic’s name into disrepute. This is something the club will not tolerate and we therefore have no other option but to take this action.
"We will not allow the great name of Celtic to be damaged in this way any more - our supporters deserve more than this.
"While recent events are very regrettable, we would like to thank our many thousands of fans for the wonderful, positive backing which they continue to give to Celtic. We are sure these supporters will understand the position which the club is in and we are also sure they will unite with the club as we move forward.
"Celtic Football Club is in excellent shape on and off the field. The club is in a very safe and strong position and we have a young, exciting team working hard to deliver quality football and success for our supporters, as they did on Friday evening with a magnificent performance. This is what we want to be talking about and this is what we want to celebrate.
"Celtic has a proud 125-year history and fundamental to that history have been our fans. Our supporters enjoy a wonderful reputation earned across many years, many families and many generations. This is something we must protect vigorously."
Police Scotland made no arrests inside Fir Park but have said they are reviewing CCTV footage to identify those responsible.
They confirmed the use of 18 smoke bombs, three fireworks and one flare.
Earlier on Monday, SPFL chief executive Neil Doncaster condemned the behaviour of Celtic supporters as the league started an investigation into events.
He said: "We have already been in touch with both clubs and the police following the disturbances during Friday night’s fixture at Fir Park.
"We absolutely condemn this type of behaviour. It has no place in the game.
"We are confident that the police and both clubs will play a full part in helping to identify those involved in what were shameful scenes.
"We expect the SPFL Match Delegate report to be with us within the next 24 to 48 hours.
"The SPFL will work closely with our colleagues at both clubs and with the police as part of a thorough investigation into Friday night’s events."
STV understands a decision on whether action will be taken by the league is expected to be made within the next seven days.