Lebanon's Australia-based players have said they intend to put tape over the logo in protest at the way the federation is running the game in the West Asian country.
The action is being led by some of the team's most prominent players including the National Rugby League's Robbie Farah, Josh Mansour and Mitch Moses.
The trio and other team mates were photographed in Sydney's Daily Telegraph newspaper with the logos covered up.
In response, the federation (LRLF) said in a statement it would not "tolerate any insult to the iconic, national symbol of the Republic of Lebanon and its people.
"The Lebanese public prosecutor’s office has been made aware of the incident and will launch an investigation in coordination with the LRLF," the statement added.
"It is a criminal offence to denigrate the national emblem of the Republic of Lebanon."
The statement also said players would be charged with misconduct, and the LRLF would administer suspensions and seek "significant monetary fines" if players were found guilty.
Lebanon were surprise quarter-finalists at the 2017 Rugby League World Cup hosted by champions Australia, New Zealand and Papua New Guinea.
Farah, who represented Lebanon at the 2017 tournament, said the 'Cedars' players were taking a stand because they did not support the current board or how it was elected.
"We want what's best for the long-term future of the game in Lebanon,” he told the Daily Telegraph.
The LRFL said its board was elected "according to Lebanese sports law".
(Reporting by Ian Ransom; Editing by Peter Rutherford)
