The move comes after the behaviour of fans during Friday night's match at Motherwell.
Supporters ripped out seats, and threw flares and smoke bombs onto the pitch, at Fir Park.
Club bosses today said they were "appalled" by fans' actions.
After the SPFL condemned the "shameful scenes", Celtic decided to take action against those they deem responsible.
In a statement, the club said: "Celtic 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."
The statement added: "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."