The incident allegedly took place during Rangers' 2-1 victory over Premiership champion Celtic on 29 December.
The boy cannot be named for legal reasons, Police Scotland confirmed.
"Abuse of any form is completely unacceptable and Police Scotland will continue to rigorously investigate any reports of abuse we receive and bring those responsible before the relevant authorities," Superintendent Mark Sutherland of Greater Glasgow Division said. "We'd remind the public that, as the person charged is below the age of 18, he cannot be named or identified for legal reasons as per the Criminal Procedure (Scotland) Act 1995."
Rangers claimed their first league win at Celtic Park since 2010 thanks to goals from Ryan Kent and Nikola Katic either side of an Odsonne Edouard equaliser.
Rangers striker Alfredo Morelos was sent off in second-half injury time after receiving a second yellow card for simulation.