Both clubs will also have to pay £100,000 to the team they are drawn against in that fixture as compensation for the fact that no gate money will accrue to them.
Celtic, according to McLaughlin, have reacted to the sanctions, saying they are “disproportionate” and that the club is shocked, while Rangers have yet to react.
Fans clashed on the Ibrox pitch after Celtic secured a 4-2 shoot-out victory over Rangers in the Scottish Gas Scottish Cup on penalties.
Police have made 37 arrests following the violence, which saw officers, supporters, members of coaching staff, and players assaulted.
A ten-year-old child was also struck by a coin as items, including pyrotechnics, were thrown by supporters.
A recent report by the Scottish Football Association following the incident found that “life-threatening” violence could have unfolded in the four minutes and 28 seconds it took for police to re-establish control after the disorder broke out.
Now, both clubs have been ordered to play their next Scottish Cup home games behind closed doors.
Both clubs have the right to appeal.
A report by the SFA on the disorder found that Celtic Ultras were the first to enter the pitch “in jubilation”, with others following their lead.
It added: “The post-match pitch invasion by several hundred Celtic supporters was wholly inexcusable. It provoked an immediate hostile response from sections of the home support, who forced past stewards and police to reach the pitch.”
Amid the disorder, a flare was thrown between the two groups six times, with one striking an RFC security operative and a CCTV operator.
The stand manager was found to have been confronted by a masked Rangers fan – assumed to be an Ultra group member – and hit in the face and hospitalised. The employee is receiving ongoing treatment for the inner ear following a traumatic injury.
Celtic said in a statement: “‘We are shocked by this disproportionate punishment for a relatively small incursion by Celtic supporters at a moment of emotion and celebration.
“Our club has never defended supporters entering the field of play, and we have repeatedly taken action when it occurs.
“However, we understand the part emotion plays in football and would have expected the context and distinction in behaviours to have been taken into account by the Panel.
“Another important distinction is that, on this occasion, Celtic were not the home club, responsible for stadium safety arrangements.
“We will study the panel’s report and reasoning when it is available and will thereafter consider our next steps.”
The two clubs could also face a second home match without fans if there is a further incident of either side’s supporters engaging in “unacceptable conduct” in a Scottish Cup fixture.
The sanctions are likely to come into force when both sides enter this season’s Scottish Cup at the fourth-round stage in the middle of January.
Police create cordon on pitch to separate Old Firm fans last seasonBoth clubs gave evidence to an independent judicial panel after being charged under the Scottish FA’s disciplinary rule 37, which covers unacceptable conduct at matches.
An independent review published last month concluded the incident came within a “very small margin” of becoming a violent mass confrontation.
The report, led by Mark Blackbourne, identified failings by both clubs and criticised the Scottish FA for not taking a tougher approach to crowd disorder.
In the recent past, the SFA and SPFL have handed down fines and, on occasion, reduced ticket allocations for issues such as the use of pyrotechnics, but the severity of this sanction signals a shift in approach.
The SFA has not escaped its share of the criticism by the independent review, but the panel’s report provided the governing body with the cover it needed to get tougher on an ever-growing problem.
And while it comes as no surprise to see the clubs defending their positions, when the dust settles, the SFA will hope that these sanctions will send out a clear message that unacceptable conduct will no longer be tolerated.
Scottish Labour Justice spokesperson Pauline McNeill, left, said: “The violence and disorder at the Old Firm match last season was completely and utterly unacceptable.