The club announced the sanctions following Friday night's Scottish Premiership match at Motherwell, which saw seats ripped out and smoke bombs thrown on to the pitch.
It also follows several controversies involving the self-styled "ultras" and banners referring to the Republican hunger strikes in Northern Ireland's Maze Prison more than 30 years ago.
A total of 250 season ticket holders located in Section 111, where the Green Brigade is seated at Celtic Park, will be moved elsewhere in the stadium. In addition, 128 fans have been banned pending investigation by the club.
Celtic Park sources said all those sold tickets to the Motherwell game from the Green Brigade section were bunched together near police observation points but moved during the match. These are understood to be the fans suspended.
By last night some of those suspended had taken to social media to deny being at the game at Fir Park. Interviews will take place in the coming days to eliminate those not there.
Celtic's statement read: "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 have no other option but to take this action."
Police Scotland made no arrests inside Fir Park but has said it is reviewing CCTV footage to identify those responsible.
Meanwhile, Police Scotland said it had received complaints of a "death list" posted online by Rangers supporters of individuals its sees as being opposed to the club.
The Vanguard Bears, who have close links with loyalist groups in Belfast, posted an image showing journalists, politicians and people involved in football, with the faces of late QC Paul McBride and Paul McConville, a solicitor who passed away last month, crossed out.
A Police Scotland spokeswoman said inquiries were ongoing.