The trade union said it knows of approximately 30 cases in recent months where patients were driven to hospital in police cars because of a lack of available ambulances or long waits for paramedics.
Last month the army was called in to help drive ambulances amid deteriorating response times and warnings about driver shortages.
But now the police federation has revealed officers are also being asked to attend medical emergencies and have helped by taking patients to hospital in the absence of ambulances.
The Scottish Ambulance Service has denied the claims.
Examples recorded by Police Scotland officers – as reported by the 1919 Magazine – included an unconscious man who had attempted to take his own life by overdose being driven to hospital in a police car because no ambulance had attended more than an hour after being called.
Another incident involved an elderly man lying on a pavement with a leg injury and in “extreme confusion”, according to the police report, with his foot turning black.
More than five and a half hours after a 999 call was made, and with all ambulances unavailable, he was put in the back of an “extremely uncomfortable” police van and taken to hospital.
A third case was the ambulance service reportedly calling for the police to help with a woman whose motorbike had fallen on her, leaving her with an open compound fracture of her lower leg.
The police log read: “A local off duty nurse is with her but as the ambulance will not be able to attend for two hours the SAS (Scottish Ambulance Service) let us know, despite it being a medical matter and their lack of resources doesn’t change what it is.
“They ask if we can attend (not sure what for) however the duty sergeant has no units and not sure what assistance they could be if he did.”
Gordon Forsyth from the Scottish Police Federation said: “Cops out there are taking people to hospital in the back of police cars simply because the ambulance is going to be hours, or there isn’t anybody suitable to leave the person with and stand down.
“I’ve got a list of 30-odd examples, various things where the cops have been sent to calls because an ambulance hasn’t been available, or having to wait for a significant period of time for an ambulance to get there.
“It all goes back to the question of: where does the policing responsibility stop and start?”
In response, a spokeswoman for the Scottish Ambulance Service said: “We do not ask Police officers to attend emergency situations instead of an ambulance crew or transport patients to hospital.
“For all 999 calls, the ambulance service will always dispatch the nearest, most appropriate response.”
Scottish Conservative health spokesman Dr Sandesh Gulhane said: “Humza Yousaf’s failure to get a grip of the crisis in the ambulance service is now having a detrimental effect on other heroic emergency service personnel.
“Humza Yousaf must produce a proper NHS Recovery plan that fully supports our ambulance service and ensures police officers do not have to be routinely diverted to supporting crews going forward.”