Celtic fans displayed banners during the win over Linfield in Glasgow
Celtic say the Green Brigade section of the club's Glasgow stadium will be closed for the next two games "amid serious safety concerns".
The club is writing to the 900 season-ticket holders affected to explain the decision and "next steps".
Uefa charged Celtic over an "illicit banner" displayed during their Champions League tie against Linfield.
Celtic chief executive Peter Lawwell said decisive action was needed in response to the fans' behaviour.
The Glasgow club have also been cited for a "kit infringement" and "blocked stairways" during Wednesday's 4-0 victory at Celtic Park.
In the aftermath, they condemned the conduct of "a small minority of the crowd".
In the past six years, the Scottish champions have been punished on 10 separate occasions relating to misconduct from supporters during European ties.
'Tarnishing club's reputation'
In a statement on Celtic's website, the club said the fans' behaviour during matches against Linfield in midweek and Hearts last season were a cause for concern.
The section will be closed for next Wednesday's Champions League qualifier against Rosenborg and against Hearts on the opening day of the Premiership season on 5 August.
"The safe standing area of the stadium had been working very well until the final game of last season against Hearts, when large numbers of flares were smuggled into and set off under banners within the Green Brigade section," Celtic said.
"It was an incredibly irresponsible and co-ordinated action which could have had tragic consequences.
"Safety of all supporters at Celtic Park is of paramount importance to the club.
"The safe operation of the safe standing area at Celtic Park requires effective communication and engagement with the supporters in that area.
"Unfortunately, due to the events at the Hearts and Linfield matches, the club is not satisfied that the Green Brigade section can be operated safely at this time."
Celtic say the Green Brigade display against Hearts was a safety risk
Celtic say they will attempt to talk to the Green Brigade about a way forward before admitting them to the section in future.
Lawwell said the behaviour of the fans in the section during the Linfield and Hearts matches amounted to a "serious safety risk".
The club's chief executive added: "There is no room for debate. The safety authorities and the football authorities make the rules. They also enforce the rules.
"If the rules are broken, Celtic will be punished again and again. There is no hiding place from these realities.
"Anyone who has Celtic's interests at heart must surely recognise them and behave accordingly.
'Celtic wake-up call'
"Every club which visits here says the atmosphere is incredible and that is something that we have worked very hard to support and encourage.
"We cannot understand why supporters who are capable of contributing so much that is positive to the club can be so reckless in doing it damage.
"In addition to the serious safety concerns, we face further Uefa disciplinary action.
"This is not a decision we have taken lightly, but the behaviour of fans in this section is posing a direct risk to the safe operation of the stadium and is also seriously tarnishing the club's hard-won reputation."
Celtic manager Brendan Rodgers expressed disappointment to be talking about "stadium safety and paramilitary banners rather than our progress into the next round of Europe".
Rodgers added that the use of pyrotechnics, unacceptable banners and ignoring stewards enforcing basic stadium safety measures "are simply not on".
"The fans have a responsibility to behave in the stadium and I would urge everyone involved to see the damage this is causing to the club," he said.
"Hopefully this is a wake-up call. The players thrive on the cauldron that the fans create at Celtic Park, but there are clearly boundaries that you can't step over."
Source: bbc.com/sport/football