Officers were called to the Phoenix Cinema in East Finchley, north London, just after 10am on Thursday following reports of criminal damage, the Metropolitan Police said.
Images shared of the cinema on social media appeared to show graffiti sprayed on its front doors which said “Say no to artwashing”.
Opened in 1912, it is thought to be the oldest cinema in continuous use in the UK.
The cinema had reportedly been due to hold a private screening of a documentary looking at the Hamas attack on the Supernova festival on October 7 last year.
No arrests have so far been made in relation to the incident.
The Met said: “While inquiries are ongoing, at this time the incident is being investigated as a potential hate crime.
“Police had already been made aware of protests expected at the venue regarding a film screening on Thursday night.
“Officers will be there to make sure those attending can protest safely whilst at the same time minimising serious disruption to the community.”
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