Aberdeen and Rangers will face each other at lunchtime on Sunday 28 October, before Celtic and Hearts square off at the same ground later in the evening with a 7.45pm kick-off.
Calum Steele is concerned that would mean officers will have to work very long hours at what is already a challenging time of year.
He told BBC Scotland’s Sportsound programme: “The one word that describes it best is just simply idiotic.
“Even if there was nothing else on that date, the police service is going to be run ragged.
“The most important thing to say is that in advance of the decision being announced, no discussions took place between the service and ourselves. The conversations that will follow will be tough indeed.
“From a police service of over 17,000 officers, having two football matches on the same day is not something that’s beyond our means but that doesn’t necessarily mean that it’s a good idea to make it happen.
“I don’t think it would be fair to suggest that fans are predisposed to violence but let’s not pretend that there aren’t a tiny minority that exist in all fan bases that can cause disproportionate demand on police resources.
“It’s going to be a highly difficult policing event in any case because of the issues associated with Halloween, fireworks, general disorder that is traditionally associated with that time of year and the fact that they’re going to be working ridiculously long hours.”