The sanctions relate to the scenes in March after Celtic's penalty shootout victory, when supporters threw fireworks and other missiles, police officers were injured and a number of arrests were made.
Both 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.

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