A 17-year-old girl and a 45-year-old man are currently being treated for injuries at Ninewells Hospital in Dundee following the incident on Monday.
The pair are expected to appear in court in the coming days.
A Police Scotland spokesperson said: “Following an incident yesterday (Monday 5 March) within a police vehicle in Perth, a 45 year old man and 17 year old woman have been arrested.
“Both are currently undergoing treatment at Ninewells Hospital in Dundee as a result of injuries sustained during the incident at Perth.
“They are expected to appear at Court from custody over the coming days, after being released from the hospital.
“Police Scotland has referred the matter to the Police Investigations and Review Commissioner.”