The 16-year-old away fan was hit during Saturday's game at Ibrox.
It is not thought the teenager was seriously hurt in the incident which happened during half-time in the Third Division game, when Rangers legends took to the pitch to celebrate the 140th anniversary of the Glasgow club's founding.
Police said the victim received medical attention in the stadium, but it is thought he was not seriously hurt.
Stirling Albion bosses have been assured by Rangers that the matter is being fully probed.
Stirling Albion operations director Stuart Brown said: "I have spoken to the head of security at Rangers and I have been assured that he is fully aware of the incident that took place during the half-time interval having been advised by the police.
"A full investigation is being undertaken, including a review of the CCTV footage.
"The police are treating this as criminal offence and if the individual or individuals concerned can be formally identified, further action will be taken."
He added that Rangers have assured him anyone found guilty of such an offence will receive a life ban from Ibrox.
Mr Brown added: "I've been in contact with the young fan and his father to update them on developments and to offer my apologies on behalf of SAFC that he should be subjected to such a vile act, perpetrated by a mindless idiot for whom I hold nothing but contempt."
Police were made aware of the incident at about 4pm on Saturday.
A police spokes- woman said: "We will be examining CCTV. "
A spokesman for Rangers said: "The club is assisting police with their investigation."
The incident came a day before Manchester United's Rio Ferdinand was struck by a coin during an English Premier League game with Manchester City.