In a bid to ensure the service's neutrality, officers have also been forbidden from wearing referendum-related T-shirts.
Calum Steele, the general secretary of the Scottish Police Federation, described the new rules as "perverse".
Under existing regulations, officers are not allowed to take "any active part in politics". New guidance issued by the force has explained what this means in the context of the referendum.
Officers must not "attend events" which could be perceived as "benefiting a particular party", or comment on "political policy or proposals".
They have also been told to "carefully consider" their online activity and are prevented from wearing badges and "associated material". In addition, officers cannot "encourage any member of the public to vote".
One police source told this newspaper: "The regulations say cops are banned from an 'active' part in politics, not any part. This new guidance is way over the top."
By contrast, civilian staff have only been banned from wearing badges and T-shirts when on duty.
Steele said: "The guidance goes much too far. It suggests police officers can't even talk to each other about the referendum, or go to events.
"It would be perverse if police officers were uniquely excluded from being involved in the biggest decision in Scotland's history.
"I've written to deputy chief constable Neil Richardson and said he should either amend or withdraw it. I've suggested the guidance goes beyond his power."
Liberal Democrat MSP Alison McInnes said: "Police officers serve the law, not a particular political party, but the referendum is not a normal election. This is the most significant vote Scots are likely to cast in our lifetimes. It is right that police officers, like the rest of us, should have the opportunity to listen to the arguments."
A Police Scotland spokesperson said: "As an apolitical organisation, police officers should refrain from undertaking any activity which could call into question the political neutrality of the police service. This includes the fact officers must not wear Yes/No badges or display any associated material such as T-shirts or other branded materials either on or off duty."