Dozens of arrests were made following clashes on the pitch after Rangers fans charged onto the pitch to confront Celtic supporters who had spilt on to celebrate their team's penalty shoot-out win in March.
Both clubs will have to pay their opponents £100,000 in compensation for the loss of shared gate receipts at the cup ties.
Any repeat of crowd trouble at Scottish Cup ties in the next two seasons could also prompt another closed-door punishment.
The Old Firm are due to meet twice in successive weekends next month with a League Cup quarter-final at Ibrox on September 13th followed by a league match at Celtic Park a week later.
An independent review into the scenes previously concluded that "crushing" and "life-threatening violence" were narrowly avoided.
Both clubs admitted charges relating to unacceptable conduct from supporters, but Celtic called the punishment "disproportionate".
In a statement, the Scottish champions said: "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."
The sanction rounds off a miserable week for both clubs after embarrassing European exits.
Celtic let a four-goal lead slip to miss out on the riches of the Champions League after a 5-1 defeat to Austrian champions LASK.
Rangers' European season is already over after defeat on penalties to Czech side Jablonec in the Conference League play-offs.