The vehicle was seen in the designated space by local lawyers and passers-by on Carlton Place next to the court last week.
"It's shocking to see the police taking up the disabled bay," said a court insider.
"It's already a busy street and parking there could have prevented someone who genuinely needed the space from using it and they might have had to park much further away."
Strathclyde Police said: "The circumstances surrounding a Strathclyde Police vehicle being parked in a disabled bay are currently being investigated.
"When details of how this vehicle came to be there are established this will be reported to the Deputy Chief Constable who will determine what action requires to be taken in respect of the officer(s) concerned.
"It has been made absolutely clear to all officers in the force that police officers are not above the law and although we are an emergency service, in anything other than exceptional circumstances, we are required to comply with the same parking, speed and road traffic restrictions as any other road user.
"When officers fail to comply with this instruction and are found to have fallen short of the standards expected of them, action will be taken."