Essex Police said it had first received a report just before 4pm on Tuesday.
A force spokeswoman said: "We have received reports of an antisemitic post on social media.
"It was reported to us just before 4pm on April 9. Our enquiries are ongoing.”
Prof Scott was head of music at the National Theatre from 2006 to 2016. He wrote original work for more than 40 plays and produced music for artists including Antony and the Johnsons and Martha Wainwright.
A National Theatre spokesperson said: “Matthew Scott is no longer employed by the National Theatre; any comments he makes on social media are in a personal capacity.
"The National Theatre has clear guidelines for current staff on acceptable use of social media in line with our diversity and inclusion policy.”
He is listed as an Emeritus Professor at Southampton University.
Prof Scott’s representative, United Agents, appears to have removed his information from its website since the Facebook post surfaced.
The JC approached Professor Scott and United Agents for comment but had not received a response when this article went live.
