Kayla, an American bald eagle, was reportedly targeted amid crowd trouble.
A joint statement issued by Charlton and the MPS read: “The Metropolitan Police Service and Charlton Athletic Football Club recognise the right of the fans to protest peacefully and both the MPS and the club continue to work together to ensure that protests take place in a way that is safe and lawful.
“Both the MPS and the club are in agreement that unlawful behaviour in the name of protest is not acceptable.
“A number of criminal acts in recent games have taken place and the club are working with the MPS to identify offenders and, where appropriate, bring them before a court for prosecution and/or seeking bans.
“When offences are committed, the MPS may not necessarily arrest at the time but can look to gather evidence and arrest or summons at a later date where appropriate.”