A statement signed by the President of Association, and copied to the Ghana News Agency, named the reporters as Malik Sulemana, Salifu Abdul Rahman and Raissa Sambou Ebu.
"We call on the Police Administration to undertake swift investigations into the incident and, for once, punish the perpetrators of such heinous crime," it stated.
The GJA explained that reports available to it indicated that a police officer riding on an unregistered motorbike hit a vehicle belonging to the Ghanaian Times near the Kinbu Traffic Lights in Accra, around 0845 today and sped off.
The police officer had allegedly jumped traffic and while meandering his way out, his motorbike hit the bumper of a Nissan saloon car, belonging to the Ghanaian Times, breaking the mirror and windscreen of the car in the process.
His pillion rider who saw what had happened beckoned him to stop, but the police officer rode on.
The driver of the Ghanaian Times' vehicle then chased and managed to block the motorbike of the police officer a few metres away from the accident scene, whereupon Malik got off the vehicle and started video-recording the incident with his mobile phone.
Angered by that action, the police officer attempted to snatch the mobile phone from the reporter and when he did not succeed, he allegedly punched the face of the reporter, as blood gushed out from his nostril.
Other police officers and a soldier in uniform allegedly joined in the beating of the reporter, pushing, kicking, slapping and punching him.
The two other reporters in the vehicle – Salifu Abdul Rahaman and Raissa Sambou Ebu – were also heckled, and in the process, Raissa, a nursing mother, collapsed and was rushed to the Greater Accra Regional Hospital for treatment.
According to the reports, the police officers demanded the mobile phone of Malik and, subsequently, handcuffed and bundled him into a police vehicle.
They then sent him to the Ministries Police Station and detained him for about four hours.
The Police were said to have ignored several pleas from the reporter to send him to hospital for medical treatment.
The reporter was later brought out of the cell and allegedly dragged on the staircase to an office on the second floor, where he was asked to write a statement.
But he declined to do so, insisting on the presence of his lawyer before proceeding.
He was then sent back into the cell, as an officer at the counter continued to hit him in the back.
It took the intervention of ACP David Eklu, the Director-General of Public Affairs Directorate of the Ghana Police Service, and ASP Efia Tenge, the Accra Region Police Public Relations Officer, to save the reporter from more torture.
"The GJA finds the assault by the said police officers barbaric in an era of rule of law when the police are supposed to be law enforcers rather than law breakers.
"We call on the Police Administration to find and punish the perpetrators of this dastardly act to serve as deterrent to others and redeem the image of the Ghana Police Service from the shameful tag of a brutish institution.
"This incident must not be added to the list of unresolved cases of assault against journalists by police officers. This culture of impunity must end now!"
It said the GJA will not relent in its efforts to seek justice for all journalists who have been assaulted by police officers in the past and urged well-meaning Ghanaians to join " in the condemnation of such barbaric conduct by the police".
"Twenty-seven years into our democratic dispensation, it is important for the police to appreciate that we live under the rule of law and not the rule of the jungle."