The artwork would be removed from the Grade I-listed building, HM Courts and Tribunals (HMCTS) said.
A spokesman added: “The Royal Courts of Justice is a listed building and HMCTS are obliged to maintain its original character.”
Defend Our Juries – which has organised protests in support of Palestine Action – claimed the artwork was a depiction of the “dystopian” proscription of the group.
“Banksy’s work of art on the walls of the Royal Courts of Justice powerfully depicts the brutality unleashed by Yvette Cooper on protesters by proscribing Palestine Action,” a spokesman said.
“We hope everyone who is moved by Banksy’s inspiring work of art will join our next action, which will be announced soon.”
The artwork was unveiled two days after 890 protesters were arrested at the protest group’s latest demonstration against Palestine Action’s proscription in Westminster.
The graffiti at the Royal Courts of Justice, which is home to the High Court and the Court of Appeal, sat beneath a CCTV camera.
Security guards were stationed beside the artwork after its discovery and it was covered with black plastic sheeting and metal barriers.
A spokesman for the Met said: “On Monday September 8, officers received a report of criminal damage to the side of the Royal Courts of Justice. Inquiries continue.”
Criminal damage carries a maximum sentence of 10 years’ imprisonment if it causes more than $5000 of damage.
Offences where the damage is worth less than $5000 have a maximum sentence of three months or a $2500 fine.
Banksy’s identity has been the source of constant speculation since his first artwork in 1999.
He made headlines last summer with his animal-themed collection in the capital, which concluded with a gorilla trying to lift a shutter at the entrance to London Zoo.
Other works included piranhas swimming in a police sentry box in the City of London and a howling wolf on a satellite dish, which was taken from the roof of a shop in Peckham, south London, less than an hour after it was spotted.
The animals collection was made up of nine works, including a rhino mounting a silver Nissan Micra, two elephant silhouettes with their trunks stretched out towards each other and three monkeys that looked as though they were swinging on a bridge.
Palestine Action was proscribed by the Government in July after supporters allegedly broke into RAF Brize Norton in Oxfordshire and damaged two aircraft.
Five people have since been charged with terror offences and remanded in custody in connection with the incident.
Last month, the co-founder of the group won the right to bring a legal challenge against proscription, arguing that the ban breached the right to freedom of expression and protest.
A judicial review over the legality of the group is due to be heard in the autumn and could result in the ban being lifted.
Banksy was approached for comment.
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