A police and army probe was launched over "concerns" raised as 400 personnel from all three forces were invited to Ibrox for a game in September.
Despite evidence that four soldiers had posed with a scarf with a sectarian slogan on it, no formal disciplinary or criminal action is being processed.
There was outrage when a video emerged from the game, which appeared to show military personnel dancing and applauding in front of singing fans before Rangers went on to win 8-0. Senior personnel from the Armed Forces looked on from the directors' box.
Police received complaints that soldiers, who had been invited to Ibrox to mark Armed Forces Day, appeared to sing sectarian songs.
A Crown Office and Procurator Fiscal Service source said there had been no prosecution report in respect of any individuals.
An Army source said the Royal Military Police, which assisted with a police investigation, had not brought any formal disciplinary charges.
The source said "administrative action" had been taken against four soldiers pictured holding a scarf with a sectarian slogan.
Administrative action is akin to having a warning.