The Scottish Premiership champions cruised to a 5-0 win at Fir Park on Friday, but the game was marred by the behaviour of a section of the away support.
Flares were let off and smoke bombs were thrown on to the pitch before and during the contest, while a number of seats in the south stand were said to have been damaged at a reported cost of £10,000 to Motherwell.
Celtic have already agreed to pay for the damage caused to that area of the stadium, although the Glasgow club could face sanctions from the Scottish Professional Football League.
And Celtic have opted to take action against the fans responsible, condemning them for bringing the club into disrepute.
A statement on Celtic's official website 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.
"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."
