The crash happened at the Keir Roundabout, at around 9.45am on Tuesday, November 23.
Police said that the army lorry had been travelling south on the A9 before the incident.
The occupants of the vehicle – two men aged 33 and 21 – were taken to Forth Valley Royal Hospital for treatment. Their injuries are serious, but are not considered life threatening.
Following the accident, police closed the road to southbound traffic. One lane has since been reopened.
Sergeant John Lang of the Road Policing Unit in Stirling said: “We are carrying out enquiries to establish the full circumstances which led to this incident.
“We would urge anyone who witnessed the incident or saw the vehicle prior to the crash to come forward if you haven’t already spoken to an officer.
“We would also be keen to speak to anyone who may have dashcam footage.
“Anyone with information can call 101, quoting incident 0670 of 23 November.”